ODE-based sampling of Markov transition kernels in flow and diffusion models

Determine how to obtain samples from the Markov transition kernel p_{t'|t}(x_{t'} | x_t) of flow matching or diffusion models using only ODE sampling, rather than relying on SDE sampling.

Background

The paper contrasts two standard sampling paradigms for flow and diffusion models: ODE sampling, which is efficient but deterministic, and SDE sampling, which provides stochastic transitions via the kernel p_{t'|t} but is significantly less efficient. Many inference-time reward alignment algorithms depend on drawing samples from p_{t'|t}, making the lack of an ODE-based approach a practical bottleneck.

This explicit unknown motivates the introduction of GLASS Flows, which construct an "inner" flow matching model enabling ODE-based sampling of a broad class of Markov transitions, including the posterior and DDPM transitions, without additional training. The statement reflects the gap that previously existed prior to the method proposed in this work.