Tilt Matching for Scalable Sampling and Fine-Tuning

We propose a simple, scalable algorithm based on stochastic interpolants for sampling from unnormalized densities and for fine-tuning generative models. The approach, Tilt Matching, arises from a dynamical equation relating the flow matching velocity to one targeting the same distribution tilted by a reward, implicitly solving a stochastic optimal control problem. The resulting velocity inherits the regularity of stochastic interpolant transports while minimizing an objective with strictly lower variance than flow matching itself. The update to the velocity field can be interpreted as the sum of all joint cumulants between the interpolant velocity and the reward, and to first order is their covariance. The method requires neither reward gradients nor backpropagation through trajectories of the flow or diffusion. We empirically demonstrate that the approach is efficient and highly scalable, providing state-of-the-art results on sampling under Lennard-Jones systems and competitive performance for fine-tuning Stable Diffusion, without requiring reward multipliers. The framework also applies directly to tilting few-step flow map models.

Many generative AI systems can create images, molecules, or other complex data, but it is often hard to make them produce outputs that satisfy a specific goal. For example, scientists may want to generate molecular configurations that satisfy specific physical constraints, or users may want an image model to better follow a text prompt. We introduce Tilt Matching, a method for adapting an existing generative model so that it favours high-scoring outputs according to a given scoring rule. The key idea is to update the model’s path from noise to realistic samples using simple learning steps that gradually shift it toward better outputs. This makes the method easier to scale and more stable in practice. In experiments, Tilt Matching improved sampling for molecular physics benchmarks and competitively fine-tuned Stable Diffusion 1.5, suggesting a practical way to adapt powerful generative models to new scientific and creative goals when direct training data is limited.