2508.19982

# Diffusion Language Models Know the Answer Before Decoding **Authors**: - Soroush Vosoughi, Shiwei Liu (The Hong Kong Polytechnic University  Dartmouth College  University of Surrey  Sun Yat-sen University) ## Abstract Diffusion language models (DLMs) have recently emerged as an alternative to autoregressive approaches, offering parallel sequence generation and flexible token orders. However, their inference remains slower than that of autoregressive models, primarily due to the cost of bidirectional attention and the large number of refinement steps required for high-quality outputs. In this work, we highlight and leverage an overlooked property of DLMs— early answer convergence: in many cases, the correct answer can be internally identified by half steps before the final decoding step, both under semi-autoregressive and random re-masking schedules. For example, on GSM8K and MMLU, up to 97% and 99% of instances, respectively, can be decoded correctly using only half of the refinement steps. Building on this observation, we introduce Prophet, a training-free fast decoding paradigm that enables early commit decoding. Specifically, Prophet dynamically decides whether to continue refinement or to go “all-in” (i.e., decode all remaining tokens in one step), using the confidence gap between the top-2 prediction candidates as the criterion. It integrates seamlessly into existing DLM implementations, incurs negligible overhead, and requires no additional training. Empirical evaluations of LLaDA-8B and Dream-7B across multiple tasks show that Prophet reduces the number of decoding steps by up to 3.4 $×$ while preserving high generation quality. These results recast DLM decoding as a problem of when to stop sampling, and demonstrate that early decode convergence provides a simple yet powerful mechanism for accelerating DLM inference, complementary to existing speedup techniques. Our code is available at https://github.com/pixeli99/Prophet. ## 1 Introduction Along with the rapid evolution of diffusion models in various domains (Ho et al., 2020; Nichol & Dhariwal, 2021; Ramesh et al., 2021; Saharia et al., 2022; Jing et al., 2022), Diffusion language models (DLMs) have emerged as a compelling and competitively efficient alternative to autoregressive (AR) models for sequence generation (Austin et al., 2021a; Lou et al., 2023; Shi et al., 2024; Sahoo et al., 2024; Nie et al., 2025; Gong et al., 2024; Ye et al., 2025). Primary strengths of DLMs over AR models include, but are not limited to, efficient parallel decoding and flexible generation orders. More specifically, DLMs decode all tokens in parallel through iterative denoising and remasking steps. The remaining tokens are typically refined with low-confidence predictions over successive rounds (Nie et al., 2025). Despite the speed-up potential of DLMs, the inference speed of DLMs is slower than AR models in practice, due to the lack of KV-cache mechanisms and the significant performance degradation associated with fast parallel decoding (Israel et al., 2025a). Recent endeavors have proposed excellent algorithms to enable KV-cache (Ma et al., 2025a; Liu et al., 2025a; Wu et al., 2025a) and improve the performance of parallel decoding (Wu et al., 2025a; Wei et al., 2025a; Hu et al., 2025). In this paper, we aim to accelerate the inference of DLMs from a different perspective, motivated by an overlooked yet powerful phenomenon of DLMs— early answer convergence. Through extensive analysis, we observed that: a strikingly high proportion of samples can be correctly decoded during the early phase of decoding for both semi-autoregressive remasking and random remasking. This trend becomes more significant for random remasking. For example, on GSM8K and MMLU, up to 97% and 99% of instances, respectively, can be decoded correctly using only half of the refinement steps. Motivated by this finding, we introduce Prophet, a training-free fast decoding strategy designed to capitalize on early answer convergence. Prophet continuously monitors the confidence gap between the top-2 answer candidates throughout the decoding trajectory, and opportunistically decides whether it is safe to decode all remaining tokens at once. By doing so, Prophet achieves substantial inference speed-up (up to 3.4 $×$ ) while maintaining high generation quality. Our contributions are threefold: - Empirical observations of early answer convergence: We demonstrate that a strikingly high proportion of samples (up to 99%) can be correctly decoded during the early phase of decoding for both semi-autoregressive remasking and random remasking. This underscores a fundamental redundancy in conventional full-length slow decoding. - A fast decoding paradigm enabling early commit decoding: We propose Prophet, which evaluates at each step whether the remaining answer is accurate enough to be finalized immediately, which we call Early Commit Decoding. We find that the confidence gap between the top-2 answer candidates serves as an effective metric to determine the right time of early commit decoding. Leveraging this metric, Prophet dynamically decides between continued refinement and immediate answer emission. - Substantial speed-up gains with high-quality generation: Experiments across diverse benchmarks reveal that Prophet delivers up to 3.4 $×$ reduction in decoding steps. Crucially, this acceleration incurs negligible degradation in accuracy-affirming that early commit decoding is not just computationally efficient but also semantically reliable for DLMs. ## 2 Related Work ### 2.1 Diffusion Large Language Model The idea of adapting diffusion processes to discrete domains traces back to the pioneering works of Sohl-Dickstein et al. (2015); Hoogeboom et al. (2021). A general probabilistic framework was later developed in D3PM (Austin et al., 2021a), which modeled the forward process as a discrete-state Markov chain progressively adding noise to the clean input sequence over time steps. The reverse process is parameterized to predict the clean text sequence based on the current noisy input by maximizing the Evidence Lower Bound (ELBO). This perspective was subsequently extended to the continuous-time setting. Campbell et al. (2022) reinterpreted the discrete chain within a continuous-time Markov chain (CTMC) formulation. An alternative line of work, SEDD (Lou et al., 2023), focused on directly estimating likelihood ratios and introduced a denoising score entropy criterion for training. Recent analyses in MDLM (Shi et al., 2024; Sahoo et al., 2024; Zheng et al., 2024) and RADD (Ou et al., 2024) demonstrate that multiple parameterizations of MDMs are in fact equivalent. Motivated by these groundbreaking breakthroughs, practitioners have successfully built product-level DLMs. Notable examples include commercial releases such as Mercury (Labs et al., 2025), Gemini Diffusion (DeepMind, 2025), and Seed Diffusion (Song et al., 2025b), as well as open-source implementations including LLaDA (Nie et al., 2025) and Dream (Ye et al., 2025). However, DLMs face an efficiency-accuracy tradeoff that limits their practical advantages. While DLMs can theoretically decode multiple tokens per denoising step, increasing the number of simultaneously decoded tokens results in degraded quality. Conversely, decoding a limited number of tokens per denoising step leads to high inference latency compared to AR models, as DLMs cannot naively leverage key-value (KV) caching or other advanced optimization techniques due to their bidirectional nature. ### 2.2 Acceleration Methods for Diffusion Language Models To enhance the inference speed of DLMs while maintaining quality, recent optimization efforts can be broadly categorized into three complementary directions. One strategy leverages the empirical observation that hidden states exhibit high similarity across consecutive denoising steps, enabling approximate caching (Ma et al., 2025b; Liu et al., 2025b; Hu et al., 2025). The alternative strategy restructures the denoising process in a semi-autoregressive or block-autoregressive manner, allowing the system to cache states from previous context or blocks. These methods may optionally incorporate cache refreshing that update stored cache at regular intervals (Wu et al., 2025b; Arriola et al., 2025; Wang et al., 2025b; Song et al., 2025a). The second direction reduces attention cost by pruning redundant tokens. For example, DPad (Chen et al., 2025) is a training-free method that treats future (suffix) tokens as a computational ”scratchpad” and prunes distant ones before computation. The third direction focuses on optimizing sampling methods or reducing the total denoising steps through reinforcement learning (Song et al., 2025b). Sampling optimization methods aim to increase the number of tokens decoded at each denoising step through different selection strategies. These approaches employ various statistical measures—such as confidence scores or entropy—as thresholds for determining the number of tokens to decode simultaneously. The token count can also be dynamically adjusted based on denoising dynamics (Wei et al., 2025b; Huang & Tang, 2025), through alignment with small off-the-shelf AR models (Israel et al., 2025b) or use the DLM itself as a draft model for speculative decoding (Agrawal et al., 2025). Different from the above optimization methods, our approach stems from the observation that DLMs can correctly predict the final answer at intermediate steps, enabling early commit decoding to reduce inference time. Note that the early answer convergence has also been discovered by an excellent concurrent work (Wang et al., 2025a), where they focus on averaging predictions across time steps for improved accuracy, whereas we develop an early commit decoding method that reduces computational steps while maintaining quality. ## 3 Preliminary ### 3.1 Background on Diffusion Language Models Concretely, let $x_0∼ p_data(x_0)$ be a clean input sequence. At an intermediate noise level $t∈[0,T]$ , we denote by $x_t$ the corrupted version obtained after applying a masking procedure to a subset of its tokens. #### Forward process. The corruption mechanism can be expressed as a Markov chain $$ \displaystyle q(x_1:T\mid x_0) = ∏_t=1^Tq(x_t\mid x_t-1), \tag{1} $$ which gradually transforms the original sample $x_0$ into a maximally degraded representation $x_T$ . At each step, additional noise is injected, so that the sequence becomes progressively more masked as $t$ increases. While the forward process in Eq.(1) is straightforward, its exact reversal is typically inefficient because it unmasks only one position per step (Campbell et al., 2022; Lou et al., 2023). To accelerate generation, a common remedy is to use the $τ$ -leaping approximation (Gillespie, 2001), which enables multiple masked positions to be recovered simultaneously. Concretely, transitioning from corruption level $t$ to an earlier level $s<t$ can be approximated as $$ \displaystyle q_s|t \displaystyle=∏_i=1^nq_s|t({x}_s^i\mid{x}_t), q_s|t({x}_s^i\mid{x}_t)=\begin{cases}1,&{x}_t^i≠[MASK],~{x}_s^i={x}_t^i,\\[4.0pt] \frac{s}{t},&{x}_t^i=[MASK],~{x}_s^i=[MASK],\\[4.0pt] \frac{t-s}{t} q_0|t({x}_s^i\mid{x}_t),&{x}_t^i=[MASK],~{x}_s^i≠[MASK].\end{cases} \tag{2} $$ Here, $q_0|t({x}_s^i\mid{x}_t)$ is a predictive distribution over the vocabulary, supplied by the model itself, whenever a masked location is to be unmasked. In conditional generation (e.g., producing a response ${x}_0$ given a prompt $p$ ), this predictive distribution additionally depends on $p$ , i.e., $q_0|t({x}_s^i\mid{x}_t,p)$ . #### Reverse generation. To synthesize text, one needs to approximate the reverse dynamics. The generative model is parameterized as This reverse process naturally decomposes into two complementary components. i. Prediction step. The model $p_θ(x_0\mid x_t)$ attempts to reconstruct a clean sequence from the corrupted input at level $t$ . We denote the predicted sequence after this step by $x_0^t$ , i.e. $x_0^t=p_θ(x_0\mid x_t)$ . (2) ii. Re-masking step. Once a candidate reconstruction $x_0^t$ is obtained, the forward noising mechanism is reapplied in order to produce a partially corrupted sequence $x_t-1$ that is less noisy than $x_t$ . This “re-masking” can be implemented in various ways, such as masking tokens uniformly at random or selectively masking low-confidence positions (Nie et al., 2025). Through the interplay of these two steps—prediction and re-masking—the model iteratively refines an initially noisy sequence into a coherent text output. ### 3.2 Early Answer Convergency In this section, we investigate the early emergence of correct answers in DLMs. We conduct a comprehensive analysis using LLaDA-8B (Nie et al., 2025) on two widely used benchmarks: GSM8K (Cobbe et al., 2021) and MMLU (Hendrycks et al., 2021). Specifically, we examine the decoding dynamics, that is, how the top 1 predicted token evolves across positions at each decoding step, and report the percentage of the full decoding process at which the top 1 predicted tokens first match the ground truth answer tokens. In this study, we only consider samples where the final output contains the ground truth answer. For low confidence remasking, we set Answer length at 256 and Block length at 32 for GSM8K, and Answer length at 128 and Block length to 128 for MMLU. For random remasking, we set Answer length at 256 and Block length at 256 for GSM8K, and Answer length at 128 and Block length at 128 for MMLU. <details> <summary>x1.png Details</summary>  ### Visual Description ## Histogram: First Correct Answer Emergence Distribution ### Overview This image is a histogram chart illustrating the distribution of when a model first produces a correct answer during a decoding process, measured as a percentage of the total decoding steps required. The chart shows that for most samples, the first correct answer emerges later in the decoding process. ### Components/Axes * **Chart Type:** Histogram (bar chart with binned data). * **X-Axis:** Labeled **"First Correct Answer Emergence (% of Total Decoding Steps)"**. The axis is marked with major ticks at 0, 20, 40, 60, 80, and 100. The data is binned into intervals of 5% (e.g., 0-5%, 5-10%, ..., 95-100%). * **Y-Axis:** Labeled **"Number of Samples"**. The axis is marked with major ticks at 0, 25, 50, 75, 100, and 125. * **Annotations/Legend:** There is no separate legend. Key statistics are presented as text boxes with arrows pointing to specific points on the x-axis. * **Red Annotation (Position: Top-left, pointing to x=25%):** Text reads **"7.9% of samples get correct answer by 25% decoding steps"**. A red dashed vertical line extends from this annotation down to the x-axis at the 25% mark. * **Orange Annotation (Position: Top-center/right, pointing to x=50%):** Text reads **"24.2% of samples get correct answer by 50% decoding steps"**. An orange dashed vertical line extends from this annotation down to the x-axis at the 50% mark. ### Detailed Analysis The histogram displays the frequency (number of samples) for each 5% bin of decoding steps at which the first correct answer appears. **Estimated Bar Heights (Number of Samples per 5% Bin):** * 0-5%: ~10 * 5-10%: ~28 * 10-15%: ~18 * 15-20%: ~16 * 20-25%: ~12 * 25-30%: ~26 * 30-35%: ~36 * 35-40%: ~26 * 40-45%: ~34 * 45-50%: ~48 * 50-55%: ~58 * 55-60%: ~80 * 60-65%: ~66 * 65-70%: ~69 * 70-75%: ~75 * 75-80%: ~90 * 80-85%: ~90 * 85-90%: ~90 * 90-95%: ~124 (This is the tallest bar, the mode of the distribution) * 95-100%: ~41 **Trend Verification:** The visual trend shows a general increase in the number of samples as the percentage of decoding steps increases, with a notable dip in the 20-25% range. The distribution is right-skewed, with the highest concentration of samples (the peak) occurring in the 90-95% bin. **Cumulative Data from Annotations:** * By the 25% decoding step mark (red line), a cumulative total of approximately 7.9% of all samples have achieved their first correct answer. * By the 50% decoding step mark (orange line), a cumulative total of approximately 24.2% of all samples have achieved their first correct answer. ### Key Observations 1. **Late Emergence Dominates:** The tallest bar is in the 90-95% range, indicating that for a large plurality of samples, the first correct answer appears very late in the decoding process. 2. **Early Success is Rare:** The bars for the first 25% of decoding steps are relatively short, confirming the annotation that only 7.9% of samples succeed this early. 3. **Significant Increase After 50%:** The frequency of first correct answers rises sharply after the 50% mark, with the bins from 55% onward containing the majority of the samples. 4. **Bimodal-like Feature:** There is a secondary, smaller peak in the 30-35% range, suggesting a subgroup of samples that find correct answers earlier than the main cluster but later than the very early successes. ### Interpretation This histogram provides insight into the efficiency and behavior of a decoding algorithm (likely for a language model or similar system). The data suggests that the process is not efficient for the majority of cases, as most samples require over half of the total decoding steps to first produce a correct answer. The pronounced peak at 90-95% indicates a common failure mode or a point of convergence where many samples finally succeed just before the process ends. The annotations highlight critical thresholds for resource allocation. If one were to stop decoding early to save computation, stopping at 25% of steps would sacrifice 92.1% of potential correct answers, while stopping at 50% would still miss 75.8% of them. This underscores a potential trade-off between computational cost and accuracy. The distribution implies that extending the decoding budget significantly (beyond 50-60%) yields the highest marginal return in terms of the number of samples that will first succeed. </details> (a) w/o suffix prompt (low-confidence remasking) <details> <summary>x2.png Details</summary>  ### Visual Description ## Histogram: First Correct Answer Emergence in Decoding Steps ### Overview This image is a histogram chart illustrating the distribution of when a model first produces a correct answer during a decoding process, measured as a percentage of the total decoding steps allocated. The chart includes two key annotations highlighting cumulative percentages at specific thresholds. ### Components/Axes * **Chart Type:** Histogram (bar chart). * **X-Axis:** Labeled **"First Correct Answer Emergence (% of Total Decoding Steps)"**. The scale runs from 0 to 100 in increments of 20 (0, 20, 40, 60, 80, 100). The axis represents the point in the decoding process (as a percentage of total steps) where the correct answer first appears. * **Y-Axis:** Labeled **"Number of Samples"**. The scale runs from 0 to 500 in increments of 100 (0, 100, 200, 300, 400, 500). This represents the count of test samples (e.g., prompts or problems) for which the first correct answer emerged at the corresponding x-axis percentage. * **Data Series:** A single series represented by light blue bars. The bar at the far right (95-100%) is a darker shade of blue. * **Annotations:** 1. **Red Annotation (Top-Left):** A red-bordered text box stating **"59.7% of samples get correct answer by 25% decoding steps"**. A red dashed vertical line extends from this box down to the x-axis at the 25% mark. A red arrow points from the text box to this line. 2. **Orange Annotation (Top-Right):** An orange-bordered text box stating **"75.8% of samples get correct answer by 50% decoding steps"**. An orange dashed vertical line extends from this box down to the x-axis at the 50% mark. An orange arrow points from the text box to this line. ### Detailed Analysis The histogram displays the frequency distribution across bins representing 5% intervals of the decoding process (e.g., 0-5%, 5-10%, ..., 95-100%). * **Bar Values (Approximate):** * **0-5%:** ~485 samples (The tallest bar by a significant margin). * **5-10%:** ~40 samples. * **10-15%:** ~25 samples. * **15-20%:** ~25 samples. * **20-25%:** ~25 samples. * **25-30%:** ~25 samples. * **30-35%:** ~25 samples. * **35-40%:** ~30 samples. * **40-45%:** ~35 samples. * **45-50%:** ~40 samples. * **50-55%:** ~25 samples. * **55-60%:** ~20 samples. * **60-65%:** ~15 samples. * **65-70%:** ~15 samples. * **70-75%:** ~10 samples. * **75-80%:** ~5 samples. * **80-85%:** ~20 samples. * **85-90%:** ~40 samples. * **90-95%:** ~10 samples. * **95-100%:** ~75 samples (Darker blue bar). * **Trend Verification:** The distribution is heavily right-skewed. The vast majority of samples achieve their first correct answer very early (0-5% of steps). The frequency drops sharply after the first bin and remains relatively low and stable across the middle range (5-80%), with a minor, gradual increase from 35-50%. There is a small secondary peak in the final bin (95-100%). ### Key Observations 1. **Dominant Early Success:** The most striking feature is the massive concentration of samples (~485) in the 0-5% bin. This indicates that for a large portion of the dataset, the model finds the correct answer almost immediately. 2. **Cumulative Thresholds:** The annotations provide critical summary statistics: * By the 25% mark of the decoding process, 59.7% of all samples have already seen their first correct answer. * By the 50% mark, this cumulative percentage rises to 75.8%. 3. **Long Tail with a Late Peak:** While most samples succeed early, there is a long tail of samples requiring more steps. Notably, there is a small but distinct increase in samples (the darker blue bar) that only find the correct answer in the very last 5% of decoding steps (95-100%). 4. **Mid-Process Plateau:** Between roughly 5% and 80%, the number of samples per bin is relatively low and does not show a strong increasing or decreasing trend, suggesting a consistent, smaller subset of problems that require a moderate amount of decoding. ### Interpretation This histogram provides insight into the efficiency and behavior of a text generation or reasoning model during a decoding process (e.g., chain-of-thought or iterative refinement). * **What the data suggests:** The model exhibits a "quick win" pattern for the majority of cases. Over three-quarters of problems are solved within the first half of the allocated decoding budget. This implies high efficiency for a large portion of the task distribution. * **Relationship between elements:** The x-axis (progress) and y-axis (frequency) together show the temporal distribution of success. The annotations directly link specific progress milestones (25%, 50%) to the cumulative success rate, quantifying the model's early performance. * **Notable patterns and anomalies:** * **The Early Spike:** The huge initial bin suggests many problems are either very easy for the model or the model's initial reasoning is frequently correct. * **The Late Peak (95-100%):** This is a critical anomaly. It indicates a subset of problems where the model struggles significantly, only finding the correct answer after exhausting nearly all available steps. These could be the most difficult samples, cases where the model gets stuck in incorrect reasoning loops before self-correcting, or problems requiring extensive computation. * **Implication for Resource Allocation:** The data argues against using a fixed, large number of decoding steps for all samples. A dynamic stopping criterion based on confidence or verification could save significant computation for the ~76% of samples that succeed by the 50% mark, while still allowing the difficult ~24% more time. The late peak also warns that simply cutting off decoding early (e.g., at 80%) would miss the correct answers for a non-trivial number of hard cases. </details> (b) w/ suffix prompt (low-confidence remasking) <details> <summary>x3.png Details</summary>  ### Visual Description ## Histogram: First Correct Answer Emergence in Decoding Steps ### Overview This image is a histogram chart illustrating the distribution of when a model first produces a correct answer during a decoding process, measured as a percentage of the total decoding steps. The chart includes two annotated thresholds highlighting the cumulative percentage of samples that achieve correctness by specific points in the process. ### Components/Axes * **X-Axis:** Labeled "First Correct Answer Emergence (% of Total Decoding Steps)". It is a linear scale ranging from 0 to 100, with major tick marks at 0, 20, 40, 60, 80, and 100. * **Y-Axis:** Labeled "Number of Samples". It is a linear scale ranging from 0 to 150, with major tick marks at 0, 50, 100, and 150. * **Data Series:** A single data series represented by light blue vertical bars (a histogram). The bars show the frequency (count) of samples for which the first correct answer emerged within specific percentage bins of the decoding steps. * **Annotations:** 1. A **red dashed vertical line** is positioned at approximately **25%** on the x-axis. An associated red-bordered text box in the upper-left quadrant states: "88.5% of samples get correct answer by 25% decoding steps". A red arrow points from this text box to the red dashed line. 2. An **orange dashed vertical line** is positioned at approximately **50%** on the x-axis. An associated orange-bordered text box in the upper-right quadrant states: "97.2% of samples get correct answer by 50% decoding steps". An orange arrow points from this text box to the orange dashed line. ### Detailed Analysis * **Histogram Distribution:** The distribution is heavily right-skewed. The tallest bars are concentrated on the far left side of the chart, between 0% and 20% on the x-axis. * The highest bar appears in the bin just after 0%, reaching a value of approximately **140 samples**. * The next bar (around 10%) is slightly lower, at approximately **100 samples**. * The bar around 20% is at approximately **55 samples**. * The frequency drops sharply after 20%, with bars at 25%, 30%, 35%, and 40% showing progressively smaller counts (roughly 25, 20, 10, and 5 samples, respectively). * There is a very small, isolated bar at the far right end of the axis, at **100%**, representing a small number of samples (approximately **5-10**) where the first correct answer emerged only at the very last decoding step. * **Annotated Thresholds:** * The **red annotation** indicates that a cumulative **88.5%** of all samples have produced their first correct answer by the time **25%** of the total decoding steps are completed. * The **orange annotation** indicates that a cumulative **97.2%** of all samples have produced their first correct answer by the time **50%** of the total decoding steps are completed. ### Key Observations 1. **Early Convergence:** The vast majority of samples (over 88%) converge on a correct answer very early in the process, within the first quarter of the allocated decoding steps. 2. **Diminishing Returns:** After the 50% mark, only a marginal 2.8% (100% - 97.2%) of remaining samples achieve their first correct answer. The process yields correct answers for new samples at a drastically reduced rate in the second half of the decoding steps. 3. **Long Tail Outlier:** A small but non-zero number of samples (the bar at 100%) require the entire decoding budget to produce a correct answer for the first time, representing a "long tail" of difficult cases. ### Interpretation This histogram demonstrates the efficiency and behavior of a decoding algorithm (likely for a language or generative model). The data suggests the model is highly effective at finding correct solutions quickly for most inputs, as evidenced by the massive concentration of "first correct answer" events in the initial 25% of steps. The sharp drop-off after 25% and the plateau after 50% indicate that if a correct answer hasn't emerged early, the probability of it emerging later diminishes significantly. The small cluster at 100% may represent particularly challenging samples, edge cases, or potential failures where the model only stumbles upon the correct answer at the deadline. For practical application, this data could justify implementing early stopping criteria (e.g., at 50% of steps) to save computational resources with minimal loss in accuracy, as nearly all correct answers have already been found by that point. </details> (c) w/o suffix prompt (random remasking) <details> <summary>x4.png Details</summary>  ### Visual Description ## Histogram: First Correct Answer Emergence in Decoding Steps ### Overview The image is a histogram chart illustrating the distribution of when a model first produces a correct answer during a decoding process, measured as a percentage of the total decoding steps allocated. The chart includes two key cumulative performance annotations. ### Components/Axes * **X-Axis (Horizontal):** Labeled "First Correct Answer Emergence (% of Total Decoding Steps)". The scale runs from 0 to 100, with major tick marks at 0, 20, 40, 60, 80, and 100. * **Y-Axis (Vertical):** Labeled "Number of Samples". The scale runs from 0 to 500, with major tick marks at 0, 100, 200, 300, 400, and 500. * **Data Series:** A single data series represented by light blue vertical bars (a histogram). The bars show the frequency (count) of samples whose first correct answer emerged within specific percentage bins of the total decoding steps. * **Annotations:** 1. **Red Annotation (Left):** A red dashed vertical line is positioned at approximately the 25% mark on the x-axis. A red-bordered text box with an arrow pointing to this line contains the text: "94.6% of samples get correct answer by 25% decoding steps". 2. **Orange Annotation (Right):** An orange dashed vertical line is positioned at the 50% mark on the x-axis. An orange-bordered text box with an arrow pointing to this line contains the text: "97.3% of samples get correct answer by 50% decoding steps". ### Detailed Analysis * **Histogram Distribution:** The distribution is heavily right-skewed. The tallest bar is in the first bin (0-5% of steps), reaching the top of the y-axis at 500 samples. The frequency drops sharply in the subsequent bins: * Bin ~5-10%: Approximately 80 samples. * Bin ~10-15%: Approximately 20 samples. * Bin ~15-20%: Approximately 10 samples. * Bins from ~20% to ~95%: Very low frequencies, with most bins containing 0-5 samples. There is a small, isolated bar in the final bin (~95-100%), representing approximately 10-15 samples. * **Cumulative Performance:** The annotations provide cumulative statistics: * By the 25% decoding step mark, 94.6% of all samples have already achieved their first correct answer. * By the 50% decoding step mark, 97.3% of all samples have achieved their first correct answer. This indicates that only 2.7% of samples require more than half of the allocated decoding steps to first become correct. ### Key Observations 1. **Extreme Early Convergence:** The vast majority of samples (the mode) achieve their first correct answer almost immediately, within the first 5% of decoding steps. 2. **Rapid Saturation:** The cumulative performance reaches 94.6% by the 25% mark, showing that the process is highly efficient for most cases. 3. **Long Tail:** There is a very long, thin tail to the right. A small but non-zero number of samples require nearly the entire decoding budget (approaching 100%) to first produce a correct answer. 4. **Annotation Placement:** The red (25%) and orange (50%) dashed lines and their corresponding text boxes are placed in the upper portion of the chart area, clearly above the histogram bars, to avoid obscuring the data. ### Interpretation This histogram demonstrates the efficiency and behavior of a decoding or generation process (likely for a language or reasoning model). The data suggests that for the given task and model, **correct solutions emerge very early in the process for the overwhelming majority of inputs**. The process exhibits a "quick win" characteristic. The key insight is the disconnect between the *emergence of a correct answer* and the *full allocation of decoding steps*. The model often finds the correct path early but may continue generating for the full allocated budget. The small cluster of samples in the 95-100% range represents "hard" problems where the model struggles and only finds the correct answer at the very end of its allowed computation, or possibly where the correct answer is only validated as such at the final step. The jump from 94.6% at 25% steps to 97.3% at 50% steps shows diminishing returns; allocating more than 50% of the steps yields only a 2.7% gain in the proportion of samples that have *ever* been correct. This has implications for resource allocation, suggesting that early stopping criteria could be highly effective without sacrificing performance on most samples. </details> (d) w/ suffix prompt (random remasking) Figure 1: Distribution of early correct answer detection during decoding process.. Histograms show when correct answers first emerge during diffusion decoding, measured as percentage of total decoding steps, using LLaDA 8B on GSM8K. Red and orange dashed lines indicate 50% and 70% completion thresholds, with corresponding statistics showing substantial early convergence. Suffix prompting (b,d) dramatically accelerates convergence compared to standard prompting (a,c). This early convergence pattern demonstrates that correct answer tokens stabilize as top-1 candidates well before full decoding. I. A high proportion of samples can be correctly decoded during the early phase of decoding. Figure 1 (a) demonstrates that when remasking with the low-confidence strategy, 24.2% samples are already correctly predicted in the first half steps, and 7.9% samples can be correctly decoded in the first 25% steps. These two numbers will be further largely boosted to 97.2% and 88.5%, when shifted to random remasking as shown in Figure 1 -(c). II. Our suffix prompt further amplifies the early emergence of correct answers. Adding the suffix prompt “Answer:” significantly improves early decoding. With low confidence remasking, the proportion of correct samples emerging by the 25% step rises from 7.9% to 59.7%, and by the 50% step from 24.2% to 75.8% (Figure 1 -(b)). Similarly, under random remasking, the 25% step proportion increases from 88.5% to 94.6%. III. Decoding dynamics of chain-of-thought tokens. We further examine the decoding dynamics of chain-of-thought tokens in addition to answer tokens, as shown in Figure 2. First, most non-answer tokens fluctuate frequently before being finalized. Second, answer tokens change far less often and tend to stabilize earlier, remaining unchanged for the rest of the decoding process. <details> <summary>x5.png Details</summary>  ### Visual Description \n ## Legend: Token State Visualization Key ### Overview The image displays a horizontal legend or key, likely extracted from a larger chart, diagram, or visualization. It defines the meaning of four distinct color codes used to represent different states or categories of "tokens" within a process. The legend is presented as a single row of colored boxes with adjacent text labels. ### Components/Axes The legend consists of four items, arranged horizontally from left to right. Each item is composed of a colored rectangular box followed by a text label. 1. **Item 1 (Far Left):** * **Color:** White box with a thin black border. * **Label:** "No Change" 2. **Item 2 (Center-Left):** * **Color:** Solid orange box. * **Label:** "Token Change" 3. **Item 3 (Center-Right):** * **Color:** Solid blue box. * **Label:** "Token Decoded" 4. **Item 4 (Far Right):** * **Color:** Solid green box. * **Label:** "Correct Answer Token" ### Detailed Analysis * **Structure:** The legend is a simple, flat list. There is no hierarchical grouping or sub-categories indicated. * **Color Palette:** The colors are distinct and high-contrast: white, orange, blue, and green. This suggests they are chosen for clear visual differentiation in the associated main visualization. * **Text:** All text is in English, using a standard sans-serif font. The labels are concise, descriptive phrases. * **Spatial Layout:** The elements are evenly spaced in a single horizontal line. The colored boxes are all the same size and shape. ### Key Observations * The legend defines states in what appears to be a sequential or categorical process involving "tokens." * The progression of labels ("No Change" -> "Token Change" -> "Token Decoded" -> "Correct Answer Token") suggests a potential workflow or evaluation pipeline, moving from an initial state to a final, validated state. * The term "Token" is highly specific and commonly used in fields like Natural Language Processing (NLP), machine learning, cryptography, or data processing, indicating the technical context of the source material. ### Interpretation This legend is a critical component for decoding a technical visualization. It provides the semantic mapping between visual cues (colors) and conceptual states within a system that processes discrete units of data ("tokens"). * **What it suggests:** The associated chart or diagram likely tracks the transformation or validation of tokens through different stages. For example, it could visualize the attention mechanism in a transformer model, the steps of a decoding algorithm, or the audit trail of a data processing pipeline. * **Relationship between elements:** The colors create a categorical scale. "No Change" (white) likely represents a baseline or unchanged state. "Token Change" (orange) and "Token Decoded" (blue) represent intermediate processing steps. "Correct Answer Token" (green) represents the successful or target outcome. The use of green for the final state is a common convention for "correct" or "success." * **Notable implications:** The presence of a "Correct Answer Token" category implies the visualization is not just descriptive but also evaluative. It is comparing a process's output against a known ground truth or desired result. This is characteristic of visualizations used in model training, debugging, or performance analysis. Without the main chart, the specific relationships, frequencies, or sequences of these token states remain unknown, but the legend establishes the fundamental vocabulary for interpreting them. </details> <details> <summary>figures/position_change_heatmap_low_conf_non_qi_700_step256_blocklen32_box.png Details</summary>  ### Visual Description \n ## Scatter Plot: Decoding Steps vs. Output Token Position Index ### Overview The image is a scatter plot visualizing the relationship between "Decoding Steps" (x-axis) and "Output Token Position Index" (y-axis). It displays two distinct data series represented by orange and blue points, along with a green rectangular highlight. The plot appears to track the progression or activation of tokens during a decoding process, likely from a sequence generation model (e.g., a language model). ### Components/Axes - **X-axis**: Labeled "Decoding Steps". Scale ranges from 0 to 250, with major tick marks at intervals of 25 (0, 25, 50, 75, 100, 125, 150, 175, 200, 225, 250). The axis label is centered below the axis. - **Y-axis**: Labeled "Output Token Position Index". Scale ranges from 100 to 155, with major tick marks at intervals of 5 (100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155). The axis label is rotated 90 degrees and placed to the left of the axis. - **Data Series**: 1. **Orange Points**: A dense, scattered series of points. 2. **Blue Points**: A series forming a clear, diagonal line. - **Highlight**: A green rectangular box outlines a specific region of the plot. - **Legend**: No explicit legend is present in the image. The meaning of the orange and blue colors must be inferred from context. ### Detailed Analysis **1. Orange Data Series (Scatter):** * **Spatial Distribution**: The orange points are heavily concentrated in the left portion of the plot, primarily between decoding steps 0 and 125. Their density is highest in vertical bands, particularly around steps 0-25 and 50-100. * **Y-axis Range**: The points span nearly the entire y-axis range, from approximately index 100 to 155. * **Trend**: There is no single linear trend. Instead, the data shows high variability and clustering. Notable dense vertical clusters appear at: * Steps ~0-25: Points span from index ~100 to ~155. * Steps ~50-100: Points are concentrated between indices ~105 and ~145. * **Sparse Regions**: Beyond step 125, orange points become very sparse and are mostly located in the upper region (indices 100-120). **2. Blue Data Series (Line):** * **Spatial Distribution**: The blue points form a distinct, nearly perfect diagonal line. * **Trend & Key Points**: The line shows a strong, positive linear correlation. It starts at approximately **(Decoding Step: 100, Token Index: 100)** and ends at approximately **(Decoding Step: 150, Token Index: 155)**. * **Slope Calculation**: The approximate slope is (155 - 100) / (150 - 100) = 55 / 50 = **1.1**. This indicates that for each additional decoding step in this range, the output token position index increases by about 1.1 units. **3. Green Highlight Box:** * **Position & Dimensions**: The box is located in the bottom-right quadrant. Its approximate coordinates are: * Left edge: Decoding Step ~125 * Right edge: Decoding Step ~250 (extends to the plot boundary) * Bottom edge: Output Token Position Index ~145 * Top edge: Output Token Position Index ~150 * **Content**: The box specifically encloses the segment of the blue diagonal line that passes through this region, from roughly step 125 to step 150. It also contains a few sparse orange points near its left edge. ### Key Observations 1. **Two Distinct Behaviors**: The plot reveals two fundamentally different patterns: a noisy, scattered process (orange) and a clean, deterministic linear progression (blue). 2. **Phase Transition**: The blue line emerges clearly around step 100, suggesting a shift in the decoding process from a scattered, exploratory phase (orange) to a focused, sequential phase (blue). 3. **Region of Interest**: The green box highlights the final segment of the blue linear progression, possibly indicating a critical or terminal phase of the decoding sequence where token positions stabilize or follow a strict order. 4. **Asymmetry**: The orange activity is almost entirely confined to the first half of the decoding steps (0-125), while the blue line dominates the transition and later steps (100-150). ### Interpretation This visualization likely depicts the internal dynamics of an autoregressive or sequential decoding process, such as in a transformer-based language model. * **Orange Series Interpretation**: The scattered orange points may represent **attention patterns**, **hidden state activations**, or **parallel token computations** occurring during the initial, more exploratory phase of generation. The vertical clustering suggests that at certain decoding steps, the model is simultaneously considering or updating a wide range of output token positions. * **Blue Series Interpretation**: The clean diagonal line strongly suggests the **primary decoding trajectory**. It represents the sequential, step-by-step generation of output tokens, where each decoding step corresponds to advancing to the next token position in the sequence. The linearity indicates a stable, one-to-one (or near one-to-one) mapping between steps and positions in this phase. * **Green Box Significance**: The highlighted region likely marks the **finalization stage** of the sequence. The model has locked onto a specific path (the blue line) and is sequentially producing the last tokens (positions 145-150) in a deterministic manner. The absence of orange scatter here implies reduced parallelism or exploration. * **Overall Narrative**: The data suggests a two-stage decoding process: an initial **parallel/exploratory phase** (steps 0-125, orange scatter) where the model processes context and considers multiple possibilities, followed by a **sequential/execution phase** (steps 100-150, blue line) where it commits to and generates the output tokens in order. The overlap between steps 100-125 shows the transition between these modes. </details> (a) w/o suffix prompt <details> <summary>figures/position_change_heatmap_low_conf_constraint_qi_700_step256_blocklen32_box.png Details</summary>  ### Visual Description ## Scatter Plot: Decoding Steps vs. Output Token Position Index ### Overview The image is a scatter plot visualizing the relationship between "Decoding Steps" (x-axis) and "Output Token Position Index" (y-axis). It displays two distinct data series represented by orange and blue markers. A green rectangular box highlights a specific region of interest in the lower-right quadrant of the plot. The chart appears to track the progression or behavior of a sequential process, likely related to a language model's token generation or decoding algorithm. ### Components/Axes * **X-Axis:** Labeled "Decoding Steps". The scale runs from 0 to 250, with major tick marks at intervals of 25 (0, 25, 50, 75, 100, 125, 150, 175, 200, 225, 250). The axis label is positioned at the bottom center. * **Y-Axis:** Labeled "Output Token Position Index". The scale runs from 180 to 235, with major tick marks at intervals of 5 (180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235). The axis label is rotated 90 degrees and positioned on the left side. * **Data Series:** * **Orange Series:** Composed of small, square markers. These points are widely scattered across the plot area, primarily concentrated in the upper-left to central region (Decoding Steps ~0-175, Token Position ~180-215). * **Blue Series:** Composed of small, square markers. These points form a distinct, nearly linear diagonal trend descending from the top-right towards the bottom-right. * **Highlighted Region:** A green rectangular box is drawn in the lower-right quadrant. Its approximate coordinates are: * Left edge: ~Decoding Step 90 * Right edge: ~Decoding Step 250 (extending to the plot border) * Top edge: ~Token Position 222 * Bottom edge: ~Token Position 226 * **Legend:** No explicit legend is present within the image frame. The two data series are distinguished solely by color (orange and blue). ### Detailed Analysis * **Orange Data Series Trend:** The orange markers show no single, clear linear trend. They are distributed in a broad, cloud-like pattern. There is a higher density of points between Decoding Steps 0-175 and Token Positions 180-215. The distribution becomes sparser for Token Positions greater than 215 and for Decoding Steps beyond 175, though isolated points exist across the entire visible range. * **Blue Data Series Trend:** The blue markers exhibit a strong, negative linear correlation. The trend line slopes sharply downward from left to right. * The series begins at approximately (Decoding Step: 175, Token Position: 180). * It progresses diagonally, passing through approximate points like (200, 200) and (225, 225). * The series terminates at the bottom-right corner of the plot, near (Decoding Step: 250, Token Position: 235). * **Green Box Region:** This box encapsulates the terminal segment of the blue data series (from roughly Decoding Step 225 to 250) and a sparse scattering of orange points within the Token Position range of 222-226. The blue line exits the box at its bottom-right corner. ### Key Observations 1. **Distinct Behavioral Patterns:** The two colors represent fundamentally different patterns. The orange series suggests irregular, non-sequential, or parallel activity across many token positions during early-to-mid decoding steps. The blue series suggests a strict, sequential, and focused progression where one specific token position is active per decoding step in a linear fashion. 2. **Temporal Shift:** The dominant activity shifts from the scattered orange pattern to the focused blue pattern as decoding steps increase. The blue series becomes prominent after step ~175. 3. **Highlighted Termination Zone:** The green box draws attention to the final phase of the process (high decoding steps) where the sequential blue pattern concludes, and only sparse, isolated orange activity remains at a specific token position band (~222-226). 4. **Spatial Separation:** There is minimal overlap between the dense regions of the two data series. The orange cloud occupies the upper-left, while the blue line traverses the right side. ### Interpretation This plot likely visualizes the internal attention or activation patterns of a transformer-based language model during the autoregressive decoding of a sequence. * **The Orange Series** may represent "non-causal" or "parallel" attention heads or model components that are active across many future token positions simultaneously during the initial and middle phases of generation. Their scattered nature indicates they are not tied to a single, advancing decoding step. * **The Blue Series** almost certainly represents the "causal" or "autoregressive" decoding process itself. Each blue point corresponds to the model focusing on and generating the token at a specific output position (`y-axis`) at a given decoding step (`x-axis`). The perfect diagonal line confirms that at step `N`, the model is processing token `N + offset` (where the offset is ~180 in this case). * **The Green Box** highlights the end of the generation sequence. The blue line's termination indicates the model has produced the final tokens. The lingering orange points within the box might represent residual model activity or "echoes" in non-causal components even after the primary sequential generation has concluded. * **Overall Narrative:** The data suggests a two-phase process: an initial phase with broad, parallel processing (orange), followed by a focused, sequential generation phase (blue) that produces the output tokens one by one until completion. The chart effectively separates and contrasts these two modes of operation within the model's decoding trajectory. </details> (b) w/ suffix prompt Figure 2: Decoding dynamics across all positions based on maximum-probability predictions. Heatmaps track how the top-1 token changes at each position, if it is decoded at the current step, over the course of decoding. (a) Without our suffix prompts, correct answer tokens reach maximum probability at step 119. (b) With our suffix prompts, this occurs earlier at step 88, showing that the model internally identifies correct answers well before the final output. Results are shown for LLaDA 8B solving problem index 700 from GSM8K under low-confidence decoding. Gray indicates positions where the top-1 prediction remains unchanged, orange marks positions where the prediction changes to a different token, blue denotes the step at which the corresponding y-axis position is actually decoded, and green box highlights the answer region where the correct answer remains stable as the top-1 token and can be safely decoded without further changes as the decoding process progresses. ## 4 Methodology <details> <summary>x6.png Details</summary>  ### Visual Description ## Technical Diagram: Decoding Process Comparison ### Overview The image is a technical diagram comparing two decoding methods for a language model or similar AI system. It visually contrasts a standard approach with an optimized method called "Prophet with Early Commit Decoding," highlighting a reduction in computational steps. The diagram is divided into two horizontal panels labeled (a) and (b). ### Components/Axes The diagram uses a horizontal timeline format to represent sequential decoding steps. **Panel (a): Standard Full-Step Decoding** * **Title:** "(a) Standard Full-Step Decoding" * **Process Label:** "Chain-of-Thought" (purple text, top-left). * **Timeline:** A horizontal line with circular nodes at discrete time steps: `t=0`, `t=2`, `t=4`, `t=6`, and a faded node at `t=10`. * **Input/Output Tokens (Purple Boxes):** Above the timeline, purple boxes show the sequence of generated tokens: * At `t=0`: `[MASK] [MASK] [MASK]` * At `t=2`: `3 sprints [MASK]` * At `t=4`: `3x3=9, 9x60=[MASK]` * At `t=6`: `3x3=9, 9x60=540` * **Answer Tokens (Orange Boxes):** Below the timeline, orange boxes labeled "Answer Tokens" show intermediate numerical results: * Below `t=0`: `3` * Below `t=2`: `60` * Below `t=4`: `5400` * Below `t=6`: `540` (This box is green, matching the final output). * **Final Output:** A dark purple box on the far right labeled "Output: 540". * **Redundant Steps:** A red dashed box encloses the timeline segment from `t=6` to `t=10`, labeled "Redundant Steps". **Panel (b): Prophet with Early Commit Decoding** * **Title:** "(b) Prophet with Early Commit Decoding" * **Timeline & Input/Output Tokens:** The sequence of purple token boxes is identical to panel (a). * **Confidence Indicator:** A long green bar spans the timeline from `t=0` to just before `t=6`, labeled "Confidence Gap > τ". * **Early Commit Point:** The green node at `t=6` is present. A green arrow originates from this node, curving upward and then rightward, bypassing the subsequent steps. * **Early Commit Label:** A yellow box along the green arrow is labeled "Early Commit Decoding". * **Final Output:** The same dark purple "Output: 540" box is connected directly by the green arrow. * **Efficiency Metric:** A green-outlined box in the top-right corner states "~55% Steps Saved". ### Detailed Analysis The diagram illustrates a computational process solving the problem: `3 sprints * (3x3=9, 9x60=540)`. The core difference lies in when the final answer (`540`) is committed to. * **Standard Method (a):** The model generates tokens sequentially. It produces the final answer token `540` at step `t=6`. However, it continues generating for four more steps (until `t=10`), which are labeled as "Redundant Steps." The "Answer Tokens" show intermediate calculations (`3`, `60`, `5400`) that appear to be part of an internal reasoning chain, with the final correct answer (`540`) appearing at `t=6`. * **Prophet Method (b):** The process is identical up to step `t=6`. The key difference is the "Confidence Gap > τ" bar, indicating the system monitors a confidence metric. Once confidence exceeds a threshold (τ) at `t=6`, it triggers "Early Commit Decoding." The model then skips the redundant steps (`t=7` to `t=10`) and directly outputs the final answer, saving approximately 55% of the decoding steps. ### Key Observations 1. **Spatial Grounding:** The "Redundant Steps" box in (a) and the "Early Commit Decoding" arrow in (b) occupy the same spatial region (right side of the timeline), visually emphasizing the replacement of wasted computation with an efficient shortcut. 2. **Color Consistency:** The final answer token `540` is consistently colored green in both panels (in the "Answer Tokens" row at `t=6`), linking it to the green "Confidence" bar and the green "Early Commit" arrow in panel (b). 3. **Trend Verification:** Both panels show the same upward trend in the complexity of generated tokens (from `[MASK]` to a full equation). The divergence is in the *termination* of the process, not in the content generated up to the commit point. 4. **Mathematical Example:** The embedded calculation (`3x3=9, 9x60=540`) serves as a concrete example of a multi-step reasoning task where the model could potentially determine the final answer before finishing all planned generation steps. ### Interpretation This diagram argues for the efficiency of the "Prophet" decoding method. It suggests that standard autoregressive decoding often performs unnecessary computation after the model has already confidently determined the correct output. The "Confidence Gap > τ" is the critical mechanism; it acts as an internal monitor that, when triggered, allows the system to abort the planned decoding schedule early. The **~55% Steps Saved** metric is a direct consequence of skipping the steps from `t=7` to `t=10`. This has significant implications for reducing latency and computational cost in real-time AI applications. The diagram implies that the "Prophet" method maintains output quality (the same "Output: 540") while dramatically improving efficiency. The use of a simple arithmetic problem makes the concept accessible, but the principle is applicable to any generative task where confidence can be measured, such as translation, summarization, or code generation. The core insight is that more generation is not always better; optimal generation should be *just enough*. </details> Figure 3: An illustration of the Prophet’s early-commit-decoding mechanism. (a) Standard full-step decoding completes all predefined steps (e.g., 10 steps), incurring redundant computations after the answer has stabilized (at t=6). (b) Prophet dynamically monitors the model’s confidence (the “Confidence Gap”). It triggers an early commit decoding as soon as the answer converges, saving a significant portion of the decoding steps (in this case, 55%) without compromising the output quality. Built upon the above findings, we introduce Prophet, a training-free fast decoding algorithm designed to accelerate the generation phase of DLMs. Prophet by committing to all remaining tokens in one shot and predicting answers as soon as the model’s predictions have stabilized, which we call Early Commit Decoding. Unlike conventional fixed-step decoding, Prophet actively monitors the model’s certainty at each step to make an informed, on-the-fly decision about when to finalize the generation. #### Confidence Gap as a Convergence Metric. The core mechanism of Prophet is the Confidence Gap, a simple yet effective metric for quantifying the model’s conviction for a given token. At any decoding step $t$ , the DLM produces a logit matrix $L_t∈ℝ^N×|V|$ , where $N$ is the sequence length and $|V|$ is the vocabulary size. For each position $i$ , we identify the highest logit value, $L_t,i^(1)$ , and the second-highest, $L_t,i^(2)$ . The confidence gap $g_t,i$ is defined as their difference: $$ g_t,i=L_t,i^(1)-L_t,i^(2). \tag{1} $$ This value serves as a robust indicator of predictive certainty. A large probability gap signals that the prediction has likely converged, with the top-ranked token clearly outweighing all others. #### Early Commit Decoding. The decision of when to terminate the decoding loop can be framed as an optimal stopping problem. At each step, we must balance two competing costs: the computational cost of performing additional refinement iterations versus the risk of error from a premature and potentially incorrect decision. The computational cost is a function of the remaining steps, while the risk of error is inversely correlated with the model’s predictive certainty, for which the Confidence Gap serves as a robust proxy. Prophet addresses this trade-off with an adaptive strategy that embodies a principle of time-varying risk aversion. Let denote $p=(T_max-t)/T_max$ as the decoding progress, where $T_max$ is the total number of decoding steps, and $τ(p)$ is the threshold for early commit decoding. In the early, noisy stages of decoding (when progress $p$ is small), the potential for significant prediction improvement is high. Committing to an answer at this stage carries a high risk. Therefore, Prophet acts in a risk-averse manner, demanding an exceptionally high threshold ( $τ_high$ ) to justify an early commit decoding, ensuring such a decision is unequivocally safe. As the decoding process matures (as $p$ increases), two things happen: the model’s predictions stabilize, and the potential computational savings from stopping early diminish. Consequently, the cost of performing one more step becomes negligible compared to the benefit of finalizing the answer. Prophet thus becomes more risk-tolerant, requiring a progressively smaller threshold ( $τ_low$ ) to confirm convergence. This dynamic risk-aversion policy is instantiated through our staged threshold function, which maps the abstract trade-off between inference speed and generation certainty onto a concrete decision rule: $$ \bar{g}_t≥τ(p), where τ(p)=\begin{cases}τ_high&if p<0.33\\ τ_mid&if 0.33≤ p<0.67\\ τ_low&if p≥ 0.67\end{cases} \tag{5} $$ Once the exit condition is satisfied at step $t^*$ , the iterative loop is terminated. The final output is then constructed in a single parallel operation by filling any remaining [MASK] tokens with the argmax of the current logits $L_t^*$ . #### Algorithm Summary. The complete Prophet decoding procedure is outlined in Algorithm 1. The integration of the confidence gap check adds negligible computational overhead to the standard DLM decoding loop. Prophet is model-agnostic, requires no retraining, and can be readily implemented as a wrapper around existing DLM inference code. Algorithm 1 Prophet: Early Commit Decoding for Diffusion Language Models 1: Input: Model $M_θ$ , prompt $x_prompt$ , max steps $T_max$ , generation length $N_gen$ 2: Input: Threshold function $τ(·)$ , answer region positions $A$ 3: Initialize sequence $x_T←concat(x_prompt,[MASK]^N_gen)$ 4: Let $M_t$ be the set of masked positions at step $t$ . 5: for $t=T_max,T_max-1,\dots,1$ do 6: Compute logits: $L_t=M_θ(x_t)$ 7: $\triangleright$ Prophet’s Early-Commit-Decoding Check 8: Calculate average confidence gap $\bar{g}_t$ over positions $A$ using Eq. 4. 9: Calculate progress: $p←(T_max-t)/T_max$ 10: if $\bar{g}_t≥τ(p)$ then $\triangleright$ Check condition from Eq. 5 11: $\hat{x}_0←argmax(L_t,dim=-1)$ 12: $x_0←x_t$ . Fill positions in $M_t$ with tokens from $\hat{x}_0$ . 13: Return $x_0$ $\triangleright$ Terminate and finalize 14: end if 15: $\triangleright$ Standard DLM Refinement Step 16: Determine tokens to unmask $U_t⊆M_t$ via a re-masking strategy. 17: $\hat{x}_0←argmax(L_t,dim=-1)$ 18: Update $x_t-1←x_t$ , replacing tokens at positions $U_t$ with those from $\hat{x}_0$ . 19: end for 20: Return $x_0$ $\triangleright$ Return result after full iterations if no early commit decoding ## 5 Experiments We evaluate Prophet on diffusion language models (DLMs) to validate two key hypotheses: first, that Prophet can preserve the performance of full-budget decoding while using substantially fewer denoising steps; second, that our adaptive approach provides more reliable acceleration than naive static baselines. We demonstrate that Prophet achieves notable computational savings with negligible quality degradation through comprehensive experiments across diverse benchmarks. ### 5.1 Experimental Setup We conduct experiments on two state-of-the-art diffusion language models: LLaDA-8B (Nie et al., 2025) and Dream-7B (Ye et al., 2025). For each model, we compare three decoding strategies: Full uses the standard diffusion decoding with the complete step budget of $T_\max$ and Prophet employs early commit decoding with dynamic threshold scheduling. The threshold parameters are set to $τ_high=7.5$ , $τ_mid=5.0$ , and $τ_low=2.5$ , with transitions occurring at 33% and 67% of the decoding progress. These hyperparameters were selected through preliminary validation experiments. Our evaluation spans four capability domains to comprehensively assess Prophet’s effectiveness. For general reasoning, we use MMLU (Hendrycks et al., 2021), ARC-Challenge (Clark et al., 2018), HellaSwag (Zellers et al., 2019), TruthfulQA (Lin et al., 2021), WinoGrande (Sakaguchi et al., 2021), and PIQA (Bisk et al., 2020). Mathematical and scientific reasoning are evaluated through GSM8K (Cobbe et al., 2021) and GPQA (Rein et al., 2023). For code generation, we employ HumanEval (Chen et al., 2021) and MBPP (Austin et al., 2021b). Finally, planning capabilities are assessed using Countdown and Sudoku tasks (Gong et al., 2024). We follow the prompt in simple-evals for LLaDA and Dream, making the model reason step by step. Concretely, we set the generation length $L$ to 128 for general tasks, to 256 for GSM8K and GPQA, and to 512 for the code benchmarks. Unless otherwise noted, all baselines use a number of iterative steps equal to the specified generation length. All experiments employ greedy decoding to ensure deterministic and reproducible results. ### 5.2 Main Results and Analysis The results of our experiments are summarized in Table 1. Across the general reasoning tasks, Prophet demonstrates its ability to match or even exceed the performance of the full baseline. For example, using LLaDA-8B, Prophet achieves 54.0% on MMLU and 83.5% on ARC-C, both of which are statistically on par with the full step decoding. Interestingly, on HellaSwag, Prophet (70.9%) not only improves upon the full baseline (68.7%) but also the half baseline (70.5%), suggesting that early commit decoding can prevent the model from corrupting an already correct prediction in later, noisy refinement steps. Similarly, Dream-7B maintains competitive performance across benchmarks, with Prophet achieving 66.1% on MMLU compared to the full model’s 67.6%—a minimal drop of 1.5% while delivering 2.47× speedup. Prophet continues to prove its reliability in more complex reasoning tasks, including mathematics, science, and code generation. For the GSM8K dataset, Prophet with LLaDA-8B obtains an accuracy of 77.9%, outperforming the baseline’s 77.1%. This reliability also extends to code generation benchmarks. For instance, on HumanEval, Prophet perfectly matches the full baseline’s score with LLaDA-8B (30.5%) and even slightly improves it with Dream-7B (55.5% vs. 54.9%). Notably, the acceleration on these intricate tasks (e.g., 1.20× on HumanEval) is more conservative compared to general reasoning. This demonstrates Prophet’s adaptive nature: it dynamically allocates more denoising steps when a task demands further refinement, thereby preserving accuracy on complex problems. This reinforces Prophet’s role as a ”safe” acceleration method that avoids the pitfalls of premature, static termination. In summary, our empirical results strongly support the central hypothesis of this work: DLMs often determine the correct answer long before the final decoding step. Prophet successfully capitalizes on this phenomenon by dynamically monitoring the model’s predictive confidence. It terminates the iterative refinement process as soon as the answer has stabilized, thereby achieving significant computational savings with negligible, and in some cases even positive, impact on task performance. This stands in stark contrast to static truncation methods, which risk cutting off the decoding process prematurely and harming accuracy. Prophet thus provides a robust and model-agnostic solution to accelerate DLM inference, enhancing its practicality for real-world deployment. Table 1: Benchmark results on LLaDA-8B-Instruct and Dream-7B-Instruct. Sudoku and Countdown are evaluated using 8-shot setting; all other benchmarks use zero-shot evaluation. Detailed configuration is listed in the Appendix. | Benchmark General Tasks MMLU | LLaDA 8B 54.1 | LLaDA 8B (Ours) 54.0 (2.34×) | Gain ( $Δ$ ) -0.1 | Dream-7B 67.6 | Dream-7B (Ours) 66.1 (2.47×) | Gain ( $Δ$ ) -1.5 | | --- | --- | --- | --- | --- | --- | --- | | ARC-C | 83.2 | 83.5 (1.88×) | +0.3 | 88.1 | 87.9 (2.61×) | -0.2 | | Hellaswag | 68.7 | 70.9 (2.14×) | +2.2 | 81.2 | 81.9 (2.55×) | +0.7 | | TruthfulQA | 34.4 | 46.1 (2.31×) | +11.7 | 55.6 | 53.2 (1.83×) | -2.4 | | WinoGrande | 73.8 | 70.5 (1.71×) | -3.3 | 62.5 | 62.0 (1.45×) | -0.5 | | PIQA | 80.9 | 81.9 (1.98×) | +1.0 | 86.1 | 86.6 (2.29×) | +0.5 | | Mathematics & Scientific | | | | | | | | GSM8K | 77.1 | 77.9 (1.63×) | +0.8 | 75.3 | 75.2 (1.71×) | -0.1 | | GPQA | 25.2 | 25.7 (1.82×) | +0.5 | 27.0 | 26.6 (1.66×) | -0.4 | | Code | | | | | | | | HumanEval | 30.5 | 30.5 (1.20×) | 0.0 | 54.9 | 55.5 (1.44×) | +0.6 | | MBPP | 37.6 | 37.4 (1.35×) | -0.2 | 54.0 | 54.6 (1.33×) | +0.6 | | Planning Tasks | | | | | | | | Countdown | 15.3 | 15.3 (2.67×) | 0.0 | 14.6 | 14.6 (2.37×) | 0.0 | | Sudoku | 35.0 | 38.0 (2.46×) | +3.0 | 89.0 | 89.0 (3.40×) | 0.0 | ### 5.3 Ablation Studies Beyond the coarse step–budget ablation above, we further dissect why Prophet outperforms static truncation by examining (i) sensitivity to the generation length $L$ and available step budget, (ii) robustness to the granularity of semi-autoregressive block updates, and (iii) compatibility with different re-masking heuristics. Together, these studies consistently show that Prophet’s adaptive early-commit rule improves the compute–quality Pareto frontier, whereas static schedules either under-compute (hurting accuracy) or over-compute (wasting steps). #### Accuracy vs. step budget under different $L$ . Table 2 (Panel A) summarizes GSM8K accuracy as we vary the number of refinement steps under two generation lengths ( $L=256$ and $L=128$ ). Accuracy under a static step cap rises monotonically with more steps (e.g., $7.7\$ for 16/32/64/128 at $L=256$ ), but still underperforms either the full-budget decoding or Prophet. In contrast, Prophet stops adaptively at $≈ 160$ steps for $L=256$ (saving $≈ 38\$ steps; $256/160≈1.63×$ ) and yields a higher score than the 256-step baseline (77.9% vs. 77.1%). When the target length is shorter ( $L=128$ ), Prophet again surpasses the 128-step baseline (72.7% vs. 71.3%) while using only $≈ 74$ steps (saving $≈ 42\$ ; $128/74≈1.73×$ ). These results reaffirm that the gains are not a byproduct of simply using fewer steps: Prophet avoids late-stage over-refinement when the answer has already stabilized, while still allocating extra iterations when needed. #### Granularity of semi-autoregressive refinement (block length). Table 3 shows that static block schedules are brittle: accuracy peaks around moderate blocks and collapses for large blocks (e.g., 59.9 at 64 and 33.1 at 128). Prophet markedly attenuates this brittleness, delivering consistent gains across the entire range, and especially at large blocks where over-aggressive parallel updates inject more noise. For instance, at block length 64 and 128, Prophet improves accuracy by $+9.9$ and $+19.1$ points, respectively. This robustness is a direct consequence of Prophet’s time-varying risk-aversion: when coarse-grained updates raise uncertainty, the threshold schedule defers early commit; once predictions settle, Prophet exits promptly to avoid additional noisy revisions. #### Re-masking strategy compatibility. Table 2 (Panel B) evaluates three off-the-shelf re-masking heuristics (random, low-confidence, top- $k$ margin). Prophet consistently outperforms their static counterparts, with the largest gain under random re-masking (+2.8 points), aligning with our earlier observation that random schedules accentuate early answer convergence. The improvement persists under more informed heuristics (low-confidence: +1.4; top- $k$ margin: +0.7), indicating that Prophet’s stopping rule complements, rather than replaces, token-selection policies. Table 2: GSM8K ablations. (a) Accuracy vs. step budget under two generation lengths $L$ . Prophet stops early (average steps in parentheses) yet matches/exceeds the full-budget baseline. (b) Accuracy under different re-masking strategies; Prophet complements token-selection policies. (a) Accuracy vs. step budget and generation length | 256 | 7.7 | 22.5 | 58.8 | 76.2 | 77.9 ( $≈$ 160; 1.63 $×$ ) | 77.1 | | --- | --- | --- | --- | --- | --- | --- | | 128 | 21.8 | 50.3 | 67.9 | 71.3 | 72.7 ( $≈$ 74; 1.73 $×$ ) | 71.3 | (b) Re-masking strategy | Random Low-confidence Top- $k$ margin | 63.8 71.3 72.4 | 66.6 72.7 73.1 | | --- | --- | --- | Table 3: Sensitivity to block length on GSM8K (semi-autoregressive updates). Prophet is less brittle to coarse-grained updates and yields larger gains as block length increases. | Baseline Ours (Prophet) $Δ$ (Abs.) | 67.1 72.8 +5.7 | 68.7 73.3 +4.6 | 71.3 72.7 +1.4 | 59.9 69.8 +9.9 | 33.1 52.2 +19.1 | | --- | --- | --- | --- | --- | --- | ## 6 Conclusion In this work, we identified and leveraged a fundamental yet overlooked property of diffusion language models: early answer convergence. Our analysis revealed that up to 99% of instances can be correctly decoded using only half the refinement steps, challenging the necessity of conventional full-length decoding. Building on this observation, we introduced Prophet, a training-free early commit decoding paradigm that dynamically monitors confidence gaps to determine optimal termination points. Experiments on LLaDA-8B and Dream-7B demonstrate that Prophet achieves up to 3.4× reduction in decoding steps while maintaining generation quality. 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Masked diffusion models are secretly time-agnostic masked models and exploit inaccurate categorical sampling. arXiv preprint arXiv:2409.02908, 2024. ## Appendix ## Appendix A Additional results <details> <summary>x7.png Details</summary>  ### Visual Description \n ## Histogram: First Correct Answer Emergence (% of Total Decoding Steps) ### Overview This image is a histogram displaying the distribution of when a "first correct answer" emerges during a decoding process, measured as a percentage of the total decoding steps. The chart includes two key annotations highlighting cumulative percentages at specific thresholds. ### Components/Axes * **Chart Type:** Histogram (bar chart showing frequency distribution). * **X-Axis (Horizontal):** * **Label:** "First Correct Answer Emergence (% of Total Decoding Steps)" * **Scale:** Linear scale from 0 to 100, with major tick marks and labels at 0, 20, 40, 60, 80, 100. * **Interpretation:** Represents the point in the decoding process (as a percentage of total steps) where the correct answer first appears. * **Y-Axis (Vertical):** * **Label:** "Number of Samples" * **Scale:** Linear scale from 0 to 200, with major tick marks and labels at 0, 50, 100, 150, 200. * **Interpretation:** Represents the count of samples (e.g., prompts, trials) for which the first correct answer emerged at the corresponding x-axis percentage. * **Annotations:** 1. **Red Box & Arrow (Position: Upper-left quadrant):** * **Text:** "15.1% of samples get correct answer by 25% decoding steps" * **Visual Cue:** A red dashed vertical line at x=25, with a red arrow pointing from the text box to this line. 2. **Orange Box & Arrow (Position: Center-right quadrant):** * **Text:** "21.4% of samples get correct answer by 50% decoding steps" * **Visual Cue:** An orange dashed vertical line at x=50, with an orange arrow pointing from the text box to this line. * **Data Series:** A single series represented by blue vertical bars. The bars appear to be grouped in bins of approximately 5% width (e.g., 0-5%, 5-10%, etc.). ### Detailed Analysis The histogram shows the frequency distribution of the emergence point for correct answers across a set of samples. * **Trend Verification:** The distribution is strongly **bimodal**. There is a very high concentration of samples where the correct answer emerges at the very beginning (0-5% of steps) and at the very end (95-100% of steps). The frequency is much lower in the middle ranges (approximately 10% to 90%). * **Approximate Data Points (Bar Heights):** * **0-5%:** ~215 samples (The tallest bar, exceeding the 200 mark). * **5-10%:** ~5 samples. * **10-15%:** ~0 samples (no visible bar). * **15-20%:** ~0 samples. * **20-25%:** ~5 samples. * **25-30%:** ~10 samples. * **30-35%:** ~10 samples. * **35-40%:** ~15 samples. * **40-45%:** ~35 samples. * **45-50%:** ~35 samples. * **50-55%:** ~45 samples. * **55-60%:** ~90 samples. * **60-65%:** ~150 samples. * **65-70%:** ~150 samples. * **70-75%:** ~165 samples. * **75-80%:** ~140 samples. * **80-85%:** ~100 samples. * **85-90%:** ~50 samples. * **90-95%:** ~50 samples. * **95-100%:** ~195 samples (The second tallest bar). * **Annotation Data:** The annotations provide cumulative statistics: * By the 25% mark of the decoding process, 15.1% of all samples have already produced their first correct answer. * By the 50% mark, 21.4% of all samples have produced their first correct answer. ### Key Observations 1. **Bimodal Distribution:** The most striking feature is the U-shaped or bimodal distribution. A large proportion of samples either succeed almost immediately or require nearly the full decoding budget. 2. **Low Mid-Range Frequency:** Very few samples have their first correct answer emerge in the first half of the process (0-50%), as confirmed by the low cumulative percentage (21.4%) at the 50% mark. 3. **Late-Stage Surge:** There is a significant increase in samples achieving their first correct answer in the latter half of the process, particularly from 60% onward. 4. **Annotation Discrepancy:** The red annotation states "15.1% of samples get correct answer by 25% decoding steps." Visually summing the approximate bar heights from 0% to 25% (215 + 5 + 0 + 0 + 5) yields ~225 samples. If the total sample count is around 1400-1500 (estimated by summing all bars), 225 would be ~15-16%, which aligns with the stated 15.1%. This confirms the annotation's accuracy. ### Interpretation This histogram suggests a **threshold or "all-or-nothing" phenomenon** in the decoding process for this task. The data does not show a normal or uniform distribution of success timing. * **Two Distinct Regimes:** The bimodality implies the existence of two primary groups of samples: "easy" ones that are solved almost instantly, and "hard" ones that require the model to exhaust nearly its entire decoding capacity before finding the correct answer. The relative lack of samples in the middle suggests a sharp divide between these regimes. * **Efficiency Insight:** The process is highly inefficient for the "hard" group, as over 78% of samples (100% - 21.4%) require more than half the decoding steps to first succeed. The model spends a significant portion of its computational effort on samples that are ultimately correct but slow to emerge. * **Potential for Optimization:** This pattern indicates a potential opportunity for adaptive decoding strategies. For instance, a system could potentially abort decoding early for samples that show no sign of success in the initial steps, reallocating resources, or employ different strategies for samples that fall into the "hard" category. The clear separation between easy and hard cases makes such a heuristic more feasible. </details> (a) MMLU w/o suffix prompt (low confidence) <details> <summary>x8.png Details</summary>  ### Visual Description ## Histogram: First Correct Answer Emergence Timing ### Overview This image is a histogram chart illustrating the distribution of when a model first produces a correct answer during its decoding process, measured as a percentage of the total decoding steps. The chart includes two key annotations highlighting the cumulative percentage of samples that have achieved a correct answer by specific decoding milestones. ### Components/Axes * **Chart Type:** Histogram (bar chart showing frequency distribution). * **X-Axis (Horizontal):** * **Label:** "First Correct Answer Emergence (% of Total Decoding Steps)" * **Scale:** Linear scale from 0 to 100. * **Major Tick Marks:** 0, 20, 40, 60, 80, 100. * **Y-Axis (Vertical):** * **Label:** "Number of Samples" * **Scale:** Linear scale from 0 to over 1500. * **Major Tick Marks:** 0, 500, 1000, 1500. * **Data Series:** A single series represented by light blue bars. * **Annotations:** 1. **Red Dashed Vertical Line:** Positioned at approximately 25% on the x-axis. * **Associated Text Box (Red Border, Top-Right):** "99.7% of samples get correct answer by 25% decoding steps" * A red arrow points from this text box to the red dashed line. 2. **Orange Dashed Vertical Line:** Positioned at approximately 50% on the x-axis. * **Associated Text Box (Orange Border, Below Red Box):** "99.9% of samples get correct answer by 50% decoding steps" * An orange arrow points from this text box to the orange dashed line. ### Detailed Analysis * **Data Distribution Trend:** The histogram shows an extreme left-skewed distribution. The vast majority of samples achieve their first correct answer at the very beginning of the decoding process. * **Bar Values (Approximate):** * The first bar, centered near 0-2% on the x-axis, is the tallest, reaching a height of approximately 1750 on the y-axis (Number of Samples). * A second, very small bar is visible between approximately 5-10% on the x-axis. Its height is very low, estimated to be around 50-100 samples. * No other bars are visible across the rest of the x-axis (from ~10% to 100%). * **Annotation Data Points:** * The red annotation indicates that by the 25% decoding step mark, 99.7% of all samples have already produced their first correct answer. * The orange annotation indicates that by the 50% decoding step mark, 99.9% of all samples have produced their first correct answer. This implies only 0.1% of samples require more than half the decoding steps to first become correct. ### Key Observations 1. **Extreme Early Success:** The model's performance is heavily concentrated at the very start of the sequence. The overwhelming majority of correct answers emerge within the first few percent of decoding steps. 2. **Near-Complete Saturation by 25%:** The 99.7% milestone at 25% steps is a critical observation, showing that the process is highly efficient and rarely needs to proceed far to find a correct solution. 3. **Negligible Late Bloomers:** The difference between 99.7% at 25% steps and 99.9% at 50% steps is only 0.2%, indicating an extremely small fraction of samples are "slow starters." 4. **Visual Confirmation:** The physical absence of any visible bars beyond the 10% mark on the x-axis visually corroborates the high percentages stated in the annotations. ### Interpretation This histogram demonstrates exceptional efficiency in the model's decoding or generation process for the given task. The data suggests that the model's mechanism for arriving at a correct answer is highly effective and operates decisively at the outset. * **Performance Implication:** The model does not typically require extensive "search" or many iterative steps to find a correct solution. Success is almost immediate. * **Resource Allocation:** From a systems perspective, this could imply that computational resources (like decoding steps) could be safely capped at a much lower percentage (e.g., 25-30%) without sacrificing accuracy for the vast majority of cases, potentially leading to significant efficiency gains. * **Underlying Mechanism:** The pattern is indicative of a model that either has very strong initial priors or confidence, or whose correct reasoning paths are readily accessible early in its generation sequence. The near-total lack of a "long tail" in the distribution is a notable and positive characteristic for reliability and predictability. </details> (b) MMLU w/ suffix prompt (low confidence) <details> <summary>x9.png Details</summary>  ### Visual Description ## Histogram: First Correct Answer Emergence Distribution ### Overview The image is a histogram chart illustrating the distribution of when a model first produces a correct answer during a decoding process, measured as a percentage of the total decoding steps. The chart includes two key annotations highlighting cumulative percentages at specific thresholds. ### Components/Axes * **Chart Type:** Histogram (bar chart). * **X-Axis:** * **Title:** "First Correct Answer Emergence (% of Total Decoding Steps)" * **Scale:** Linear scale from 0 to 100, with major tick marks at 0, 20, 40, 60, 80, 100. * **Y-Axis:** * **Title:** "Number of Samples" * **Scale:** Linear scale from 0 to 800, with major tick marks at 0, 200, 400, 600, 800. * **Data Series:** A single series represented by light blue vertical bars. The height of each bar represents the count of samples whose first correct answer emerged within that percentage bin. * **Annotations:** 1. **Red Dashed Vertical Line & Box (Position: Top-Left quadrant, line at x=25):** * **Text:** "95.3% of samples get correct answer by 25% decoding steps" * **Visual Cue:** A red arrow points from the text box down to the dashed line. 2. **Orange Dashed Vertical Line & Box (Position: Center-Right, line at x=50):** * **Text:** "99.2% of samples get correct answer by 50% decoding steps" * **Visual Cue:** An orange arrow points from the text box left to the dashed line. * **Background:** White with a faint gray grid. ### Detailed Analysis * **Distribution Shape:** The histogram is strongly right-skewed. The tallest bar is at the far left (0-5% bin), indicating the highest frequency of samples achieve their first correct answer very early in the decoding process. * **Bar Height Trends (Approximate Values):** * **0-5% bin:** ~820 samples (tallest bar). * **5-10% bin:** ~330 samples. * **10-15% bin:** ~210 samples. * **15-20% bin:** ~90 samples. * **20-25% bin:** ~40 samples. * **25-30% bin:** ~30 samples. * **30-35% bin:** ~10 samples. * **Bins beyond 35%:** Bars are very short, approaching zero, indicating very few samples require more than 35% of decoding steps for their first correct answer. * **Key Thresholds (from annotations):** * By the **25%** mark on the x-axis, **95.3%** of all samples have already achieved their first correct answer. * By the **50%** mark on the x-axis, **99.2%** of all samples have achieved their first correct answer. ### Key Observations 1. **Extreme Early Success:** The vast majority of correct answers emerge in the first quarter of the decoding process. The distribution is heavily concentrated between 0% and 20%. 2. **Diminishing Returns:** After the 25% threshold, the number of new samples achieving their first correct answer drops precipitously. The tail of the distribution beyond 35% is negligible. 3. **High Cumulative Coverage:** The two annotations confirm that nearly all samples (99.2%) succeed by the halfway point of the decoding steps, suggesting the process is highly efficient for the evaluated task. ### Interpretation This histogram demonstrates the efficiency and early convergence of the decoding process being analyzed. The data suggests that for the given task and model, the correct solution is typically found very early. The "first correct answer" is not evenly distributed over time but is heavily front-loaded. The 95.3% and 99.2% thresholds are critical performance metrics. They indicate that allocating computational resources (decoding steps) beyond 50% yields minimal additional success, as only 0.8% of samples require more than half the steps. This has practical implications for optimizing inference speed and cost: one could potentially truncate the decoding process early (e.g., at 50% of a predefined maximum step count) with a very high probability of having already obtained the correct answer for nearly all inputs. The chart effectively argues that the model's "thinking" or search process is highly effective in its initial stages for this specific evaluation. </details> (c) MMLU w/o suffix prompt (random) <details> <summary>x10.png Details</summary>  ### Visual Description ## Histogram: First Correct Answer Emergence in Decoding Steps ### Overview The image is a histogram chart analyzing the point at which a model first produces a correct answer during a decoding process. The chart demonstrates that the vast majority of samples achieve a correct answer very early in the process, with near-total correctness achieved well before the full decoding budget is exhausted. ### Components/Axes * **Chart Type:** Histogram. * **X-Axis:** Titled **"First Correct Answer Emergence (% of Total Decoding Steps)"**. It is a linear scale ranging from 0 to 100, with major tick marks at 0, 20, 40, 60, 80, and 100. * **Y-Axis:** Titled **"Number of Samples"**. It is a linear scale ranging from 0 to over 1500, with major tick marks at 0, 500, 1000, and 1500. * **Data Series:** A single data series represented by light blue histogram bars. The distribution is heavily right-skewed. * **Annotations:** Two vertical dashed lines with associated text boxes provide cumulative statistics. * **Red Dashed Line:** Positioned at approximately **25%** on the x-axis. An arrow points from a red-bordered text box to this line. * **Orange Dashed Line:** Positioned at approximately **50%** on the x-axis. An arrow points from an orange-bordered text box to this line. ### Detailed Analysis * **Histogram Distribution:** * The tallest bar is in the **0-5%** bin, with a height of approximately **1650 samples**. This indicates the largest group of samples gets the correct answer almost immediately. * The second bar (5-10% bin) is significantly shorter, at approximately **100 samples**. * The third bar (10-15% bin) is very short, at approximately **50 samples**. * Bars beyond the 15% mark are negligible or not visible, showing that very few samples require more than 15% of decoding steps to first achieve a correct answer. * **Annotation Text (Transcribed):** 1. **Red Text Box (Top-Left):** "98.8% of samples get correct answer by 25% decoding steps" 2. **Orange Text Box (Center-Right):** "99.6% of samples get correct answer by 50% decoding steps" ### Key Observations 1. **Extreme Early Success:** The distribution is dominated by the first bin (0-5%), showing that for the overwhelming majority of samples, the correct answer emerges at the very beginning of the decoding process. 2. **Rapid Saturation:** The cumulative statistics confirm the visual trend. By the 25% mark of the total allowed decoding steps, 98.8% of all samples have already found a correct answer. This leaves only 1.2% of samples unresolved at that point. 3. **Diminishing Returns:** The improvement from the 25% checkpoint to the 50% checkpoint is minimal (from 98.8% to 99.6% correct), indicating that allocating more than 50% of the decoding budget yields almost no additional correct answers for this dataset and model configuration. 4. **Long Tail Absence:** There is no visible long tail in the histogram. The process either succeeds very quickly or, for a tiny fraction of samples, does not succeed within the observed range. ### Interpretation This chart provides strong evidence for the **efficiency** of the decoding or generation process being evaluated. The data suggests the model is highly confident and accurate in its early steps for this particular task. * **Performance Implication:** The primary takeaway is that the model's "first correct answer" is not a late-stage correction but an early-stage success. This has implications for resource allocation; one could potentially truncate the decoding process early (e.g., at 25-50% of the steps) with minimal loss in accuracy, leading to significant computational savings. * **Underlying Behavior:** The pattern indicates that for most inputs, the model's initial reasoning or generation path is correct. The few samples that take longer (the small bars between 5-15%) might represent more complex or ambiguous cases where the model explores incorrect paths before converging on the right answer. * **Anomaly Note:** The near-total correctness (99.6%) by the 50% mark is a notable result. It suggests that for this specific benchmark or task, the problem of "never finding the correct answer" is almost non-existent within the given decoding budget. The remaining 0.4% of samples may represent fundamental failures or edge cases the model cannot handle. </details> (d) MMLU w/ suffix prompt (random) Figure 4: Distribution of early correct answer detection during decoding process. Histograms show when correct answers first emerge during diffusion decoding, measured as percentage of total decoding steps, using LLaDA 8B on MMLU. Red and orange dashed lines indicate 50% and 70% completion thresholds, with corresponding statistics showing substantial early convergence. Suffix prompting (b,d) dramatically accelerates convergence compared to standard prompting (a,c). This early convergence pattern demonstrates that correct answer tokens stabilize as top-1 candidates well before full decoding. Table 4: Configurations used in our runs. We keep only parameters relevant to our method: base budget $(L,T,B)$ and Prophet ’s confidence schedule. | MMLU | $L{=}64, T{=}64, B{=}16$ | $(7.5, 5.0, 2.5)$ | 33%, 67% | | --- | --- | --- | --- | | ARC-C | $L{=}64, T{=}64, B{=}16$ | $(7.5, 5.0, 2.5)$ | 33%, 67% | | Hellaswag | $L{=}64, T{=}64, B{=}16$ | $(7.5, 5.0, 2.5)$ | 33%, 67% | | TruthfulQA | $L{=}64, T{=}64, B{=}16$ | $(7.5, 5.0, 2.5)$ | 33%, 67% | | WinoGrande | $L{=}64, T{=}64, B{=}16$ | $(7.5, 5.0, 2.5)$ | 33%, 67% | | PIQA | $L{=}64, T{=}64, B{=}16$ | $(7.5, 5.0, 2.5)$ | 33%, 67% | | GSM8K | $L{=}256, T{=}256, B{=}32$ | $(8.0, 5.0, 3.5)$ | 33%, 67% | | GPQA | $L{=}256, T{=}256, B{=}32$ | $(8.0, 5.0, 3.5)$ | 33%, 67% | | HumanEval | $L{=}512, T{=}512, B{=}32$ | $(7.5, 5.0, 4.5)$ | 33%, 67% | | MBPP | $L{=}512, T{=}512, B{=}32$ | $(7.5, 5.0, 4.5)$ | 33%, 67% | | Sudoku | $L{=}24, T{=}24, B{=}24$ | $(7.5, 5.0, 2.5)$ | 33%, 67% | | Countdown | $L{=}32, T{=}32, B{=}32$ | $(7.5, 5.0, 2.5)$ | 33%, 67% | ## Appendix B Evaluation Details We re-implemented the evaluation of LLaDA and Dream on those reported datasets. We generate and extract the final answer instead of comparing the log probability in the multiple-choice setting, which can lower the reported scores on some datasets because the model sometimes fails to produce an answer in the given format. The configuration of each experiment is summarized in Table 4.