New paper unifies diffusion, score-based, and flow matching models under one theory

A new 62-page arXiv paper from Aditya Ranganath and Mukesh Singhal offers a unified measure-theoretic framework that brings together three of the most influential generative modeling paradigms: diffusion models, score-based generative models, and flow matching. The authors show that despite fragmented notation and competing derivations, all three methods are instances of learning a time-dependent vector field that induces a family of marginals \(\rho_t\) governed by continuity and Fokker-Planck equations. Within this unified view, the paper (i) derives reverse-time sampling for diffusion and score-based models as controlled stochastic dynamics, (ii) demonstrates that the probability flow ODE yields identical marginals and connects diffusion to likelihood-based normalizing flows, and (iii) interprets flow matching as direct regression of the velocity field under a chosen interpolation, clarifying when it coincides with or differs from score-based training.

The work systematically compares objectives, sampling schemes, and discretization errors under a single notation, and it explores deeper connections to Schrödinger bridges and entropic optimal transport. By exposing the shared mathematical structure, the paper helps researchers and practitioners understand practical tradeoffs around sampling speed, stability, and computational cost. It also summarizes theoretical guarantees on approximation, stability, and scalability, and outlines open problems. For anyone working with generative AI models, this survey provides a clear, rigorous map of the terrain and helps reduce the fragmentation that often obscures how these methods relate to each other.