Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Control

Diffusion models excel at capturing complex data distributions, such as those of natural images and proteins. While diffusion models are trained to represent the distribution in the training dataset, we often are more concerned with other properties, such as the aesthetic quality of the generated images or the functional properties of generated proteins. Diffusion models can be finetuned in a goal-directed way by maximizing the value of some reward function (e.g., the aesthetic quality of an image). However, these approaches may lead to reduced sample diversity, significant deviations from the training data distribution, and even poor sample quality due to the exploitation of an imperfect reward function. The last issue often occurs when the reward function is a learned model meant to approximate a ground-truth "genuine" reward, as is the case in many practical applications. These challenges, collectively termed "reward collapse," pose a substantial obstacle. To address this reward collapse, we frame the finetuning problem as entropy-regularized control against the pretrained diffusion model, i.e., directly optimizing entropy-enhanced rewards with neural SDEs. We present theoretical and empirical evidence that demonstrates our framework is capable of efficiently generating diverse samples with high genuine rewards, mitigating the overoptimization of imperfect reward models.

Feedback Efficient Online Fine-Tuning of Diffusion Models

Diffusion models excel at modeling complex data distributions, including those of images, proteins, and small molecules. However, in many cases, our goal is to model parts of the distribution that maximize certain properties: for example, we may want to generate images with high aesthetic quality, or molecules with high bioactivity. It is natural to frame this as a reinforcement learning (RL) problem, in which the objective is to fine-tune a diffusion model to maximize a reward function that corresponds to some property. Even with access to online queries of the ground-truth reward function, efficiently discovering high-reward samples can be challenging: they might have a low probability in the initial distribution, and there might be many infeasible samples that do not even have a well-defined reward (e.g., unnatural images or physically impossible molecules). In this work, we propose a novel reinforcement learning procedure that efficiently explores on the manifold of feasible samples. We present a theoretical analysis providing a regret guarantee, as well as empirical validation across three domains: images, biological sequences, and molecules.