Stratified Hazard Sampling: Minimal-Variance Event Scheduling for CTMC/DTMC Discrete Diffusion and Flow Models

• URL: http://arxiv.org/abs/2601.02799v1
• Date: Tue, 06 Jan 2026 08:19:02 GMT
• Title: Stratified Hazard Sampling: Minimal-Variance Event Scheduling for CTMC/DTMC Discrete Diffusion and Flow Models
• Authors: Seunghwan Jang, SooJean Han,
• Abstract summary: Stratified Hazard Sampling Sampling (SHS) models per-token edits as events driven by cumulative hazard (CTMC) or cumulative jump mass (DTMC)<n>SHS models per-token edits as events driven by cumulative hazard (CTMC) or cumulative jump mass (DTMC) and places events by stratifying this cumulative quantity.<n>We also introduce a phase-allocation variant for blacklist-style lexical constraints that prioritizes early edits at high-risk positions to mitigate late-masking artifacts.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: CTMC/DTMC-based discrete generative models, including uniform-noise discrete diffusion (e.g., D3PM/CTDD) and discrete flow matching, enable non-autoregressive sequence generation by repeatedly replacing tokens through a time-inhomogeneous Markov process. Inference is typically implemented with step-based simulation: each token decides to jump via independent Bernoulli (or categorical) draws at every discretization step. Under uniform-noise initialization, where self-correction requires multiple edits per position, these independent decisions induce substantial variance in both the number and timing of edits, leading to characteristic failure modes such as under-editing (residual noise) or over-editing (cascading unnecessary substitutions), decreasing reproducibility. We propose Stratified Hazard Sampling (SHS), a 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 cumulative jump mass (DTMC) and places events by stratifying this cumulative quantity: with a single random phase per position, a token jumps whenever its accumulated hazard crosses unit-spaced thresholds. This preserves the expected number of jumps while achieving the minimum possible variance among unbiased integer estimators (bounded by 1/4), without altering per-jump destination sampling and thus retaining multimodality. We also introduce a phase-allocation variant for blacklist-style lexical constraints that prioritizes early edits at high-risk positions to mitigate late-masking artifacts.

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