Systematic Hazard Sampling: Minimal-Variance Inference for Discrete Diffusion and Flow Models

Discrete diffusion models achieve strong performance in text and image generation, but their inference remains slow and must inherently balance sampling efficiency and sample quality. In this work, we present a systematic study of how the \emph{degree of stochasticity} in Markov transitions governs the sampling tradeoff. We show that highly deterministic transitions converge rapidly but suffer from error accumulation, while more stochastic transitions converge more slowly yet can achieve higher final sample quality. Using an information-theoretic analysis, we identify the underlying mechanism as an error-correcting effect induced by \emph{redundant transitions} that symmetrically exchange mass between states, and show that these transitions can provably contract sampling errors. Motivated by this analysis, we propose \emph{Discrete Churn and Restart Sampling} (DCRS), a novel inference algorithm that injects controlled stochasticity by alternating between forward and reverse diffusion processes. Experiments on synthetic datasets and large-scale benchmarks show that DCRS improves the speed-quality tradeoff in the low number of function evaluations regime. On image datasets, DCRS achieves up to a $10\times$ reduction in sampling steps compared to standard samplers while maintaining competitive sample quality, whereas on language benchmarks, we observe more nuanced behavior depending on the corruption process and sampling procedure.

Discrete diffusion models are a powerful class of generative models with strong performance across many domains. For efficiency, however, discrete diffusion typically parameterizes the generative (reverse) process with factorized distributions, which makes it difficult for the model to learn the target process in a small number of steps and necessitates a long, computationally expensive sampling procedure. To reduce the gap between the target and model distributions and enable few-step generation, we propose Forward-Learned Discrete Diffusion (FLDD), which introduces discrete diffusion with a learnable forward (noising) process. Rather than fixing a Markovian forward chain, we adopt a non-Markovian formulation with learnable marginal and posterior distributions. This allows the generative process to remain factorized while matching the target defined by the noising process. We train all parameters end-to-end under the standard variational objective. Experiments on various benchmarks show that, for a given number of sampling steps, our approach produces a higher quality samples than conventional discrete diffusion models using the same reverse parameterization.

Uniform-state discrete diffusion models update all tokens in parallel while keeping every position revisable. Even when the commonly used top-$p$ rule leaves only one candidate at a position, that choice affects only the current reverse step and can be revised at the next sampling step. We ask what changes when selected hypotheses instead become persistent context for later predictions. We therefore propose committed reveal sampling (CRS), a training-free sampler that stores selected argmax tokens and inserts them into subsequent model inputs. Our analysis gives a rationale for selecting later and for keeping selected tokens visible. Under the exact forward process, the Bayes error of selecting a clean token cannot increase as noise decreases, while in a simple latent-mode model, keeping the selected token visible helps later parallel predictions agree on the same sequence-level choice. Empirically, paired experiments on Duo-distilled then separate this persistent effect from single-step top-$p$ restriction and scalar temperature scaling. Under the same finalization rule, CRS without top-$p$ truncation reaches lower generative perplexity (GenPPL) than fixed $p=0.95$ and $p=0.9$ baselines across budgets of 8--64 function evaluations (NFE). At 64 NFE, the comparison at matched unigram entropy also gives lower GenPPL for CRS, yielding a more favorable GenPPL--entropy tradeoff. Base Duo shows the same direction in a descriptive comparison, while other diversity and continuation metrics can rank these operating points differently. These results identify support restriction and persistent context as distinct controls of that tradeoff.