New paper: exponential residual flows bring probability-flow ODEs to discrete diffusion
ArnaudDoucet1 · x · 2026-11-04
A new arXiv paper by Gourevitch, Janati, Moulines, Eric P. Xing et al. answers whether continuous diffusion's probability-flow ODE has an analogue for discrete diffusion models — affirmatively.
- Introduces exponential residual flows (ERFs): continuous residual variables per token/position evolving deterministically via piecewise ODEs whose vector fields depend on the discrete state and the diffusion's forward/backward rate matrices; discrete states change when a residual hits zero.
- Proves the construction preserves the original diffusion's marginals.
- Provides practical discretizations specialized to masked (MDM) and uniform (UDM) diffusion.
- Deterministic trajectories enable principled consistency distillation, with empirical gains on code and text generation benchmarks.
A theoretically grounded route to accelerated sampling for discrete diffusion, which the authors say can be pushed much further.
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