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

Uniform-noise discrete diffusion and flow models generate sequences non-autoregressively through iterative, context-dependent token replacements. However, these models are typically formulated as time-inhomogeneous CTMC/DTMC processes, sampled using independent Bernoulli change decisions per discretization step. This induces Poisson-binomial variance in per-position jump counts that grows with the number of required edits, leading to the common under-editing (residual noise) and over-editing (cascading substitutions) failure modes that degrade sample quality, especially under tight discretization budgets. We identify this sampler-induced variance as an orthogonal source of degradation, distinct from model-side errors and addressable purely at inference time. We propose Systematic Hazard Sampling (SHS), a training-free, drop-in, and hyperparameter-free inference principle for any sampler that admits a stay-vs.-replace decomposition. SHS models per-token edits as events driven by cumulative hazard (CTMC) or jump mass (DTMC) and triggers an edit whenever this quantity exceeds unit-spaced thresholds with a single random phase per position. For any fixed cumulative mass, this preserves the expected jump count while achieving the minimum conditional variance possible among unbiased integer estimators (at most \(1/4\)), without altering per-jump destination sampling. Experiments on four uniform-noise discrete diffusion and flow language models spanning $\sim$110M to $\sim$3B parameters show that SHS consistently improves sample quality across NFE budgets, with the gains growing with NFE as predicted by the variance gap.