  Despite Flow Matching and diffusion models having emerged as powerful
generative paradigms for continuous variables such as images and videos, their
application to high-dimensional discrete data, such as language, is still
limited. In this work, we present Discrete Flow Matching, a novel discrete flow
paradigm designed specifically for generating discrete data. Discrete Flow
Matching offers several key contributions: (i) it works with a general family
of probability paths interpolating between source and target distributions;
(ii) it allows for a generic formula for sampling from these probability paths
using learned posteriors such as the probability denoiser ($x$-prediction) and
noise-prediction ($\epsilon$-prediction); (iii) practically, focusing on
specific probability paths defined with different schedulers considerably
improves generative perplexity compared to previous discrete diffusion and flow
models; and (iv) by scaling Discrete Flow Matching models up to 1.7B
parameters, we reach 6.7% Pass@1 and 13.4% Pass@10 on HumanEval and 6.7% Pass@1
and 20.6% Pass@10 on 1-shot MBPP coding benchmarks. Our approach is capable of
generating high-quality discrete data in a non-autoregressive fashion,
significantly closing the gap between autoregressive models and discrete flow
models.
