Simulation-free and finite-time diffusion model

2026-08-04

AI Summary

This work addresses the longstanding challenge in diffusion modeling of simultaneously enabling simulation-free training and finite-time generation. The authors propose a novel reference diffusion process whose marginal distributions exactly match the target distribution, and whose time-varying conditional distributions facilitate a well-defined reversal. This formulation reveals that score matching naturally arises as the consequence of reversing the reference process and further shows that conditional flow matching corresponds to its small-noise limiting case. The resulting framework is the first to jointly support training without requiring forward simulations and generation within a finite time horizon, thereby not only broadening the theoretical foundations of diffusion models but also enhancing their practical flexibility.

Abstract

The performance of generative diffusion models is determined by the choice of the reference diffusion process connecting the empirical and prior distributions. Conventional approaches typically trade off simulation-free training against finite-time generation. We propose a framework for designing the reference process that achieves both simultaneously. The key idea is to prescribe tractable time-dependent conditional distributions and then construct the reference process realizing them as its marginals. This framework reveals that score matching is not fundamental to diffusion-model training but instead emerges naturally through reversal of the reference process. We further show that conditional flow matching arises as the small-noise limit of the proposed framework.

Problem

• diffusion models
• reference process
• simulation-free training
• finite-time generation
• score matching

Innovation

• simulation-free
• finite-time generation
• reference diffusion process
• score matching
• conditional flow matching