Tilt matching for scalable sampling and fine-tuning

ICLR 2026 Conference Submission14510 Authors

Keywords: sampling, generative modeling, flow matching, stochastic interpolants

TL;DR: scalable algorithm for sampling and fine-tuning generative models by correcting the velocity field with a novel covariance term.

Abstract: We propose a simple, scalable algorithm for using stochastic interpolants to perform sampling from unnormalized densities and for fine-tuning generative models. The approach, Tilt Matching, arises from a dynamical equation relating the velocity field for a flow matching method to the velocity field that would target the same distribution tilted by a reward. As such, the new velocity inherits the regularity of stochastic interpolant transport plans while also being the minimizer of an objective function with strictly lower variance than flow matching itself. The update to the velocity field that emerges from this simple regression problem can be interpreted as the sum of all joint cumulants of the stochastic interpolant and copies of the reward, and to first order is their covariance. We define two versions of the method, Explicit and Implicit Tilt Matching. The algorithms do not require any access to gradients of the reward or backpropagating through trajectories of the flow or diffusion. We empirically verify that the approach is efficient, unbiased, and highly scalable, providing state-of-the-art results on sampling under Lennard-Jones potentials and is competitive on fine-tuning Stable Diffusion, without requiring reward multipliers. It can also be straightforwardly applied to tilting few-step flow map models.

Primary Area: generative models

Submission Number: 14510