Discrete Flow Matching

Discrete flow matching models how a simple distribution over categories can be transformed into data such as text, graphs, or molecular sequences, offering a way to generate structured outputs through iterative refinement. Common approaches define continuous-time Markov chains and learn transition rates, using choices of coupling, noise schedule, and sampling order to shape the path; newer methods also add guidance, constraints, or distillation for faster generation. Applications include language and speech generation, molecule and biological sequence design, graph generation, and robot action prediction, often evaluated on standard task benchmarks and measures of validity, quality, and diversity. Work now spans scalable language models and practical domain-specific systems, while key challenges include reliable few-step sampling, handling constraints and variable-length structures, and understanding how training and source-distribution choices affect convergence and quality.