Diffusion / Flow Samplers

The numerical algorithm that integrates a trained diffusion or flow model from random noise into a sample, step by step.

What a diffusion or flow-matching model learns is 'which direction to move at each noise level'; actually generating a sample requires a numerical method to integrate that process forward, which is what a sampler does. In 2020, Song and colleagues wrote the diffusion process as a stochastic differential equation (SDE) and also derived a deterministic ordinary differential equation with the same marginal distributions, the probability-flow ODE: solving the SDE adds random noise at each step, while solving the ODE gives a deterministic result. Common samplers range from the simplest first-order Euler method and DDIM to specialized high-order solvers such as DPM-Solver, proposed in 2022 by Jun Zhu's team at Tsinghua, which can produce high-quality samples in roughly 10 to 20 network calls. Fewer steps means faster but less accurate, and robot policies have to trade off control frequency against action quality.

Exampleπ0's flow-matching action expert integrates with the forward Euler method over 10 steps (step size 0.1) at inference, turning a stretch of random noise into an action chunk.

Also called

ODE / SDE Solvers, Euler Sampler, DPM-Solver

Related

Diffusion Model · Flow Matching · Denoising Diffusion Implicit Model · Denoising Steps · Velocity Field · One-step Generation

Sources

Score-Based Generative Modeling through Stochastic Differential Equations (arXiv:2011.13456)
DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps (arXiv:2206.00927)
π0: A Vision-Language-Action Flow Model for General Robot Control (arXiv HTML)