Direct Distributional Optimization for Provable Alignment of Diffusion Models
This provides a provable alignment method for diffusion models, applicable to tasks like RLHF, DPO, and KTO, but it is incremental as it builds on existing distribution optimization techniques.
The paper tackles the problem of aligning diffusion models by formulating it as a distribution optimization problem and directly optimizing the distribution using the Dual Averaging method, achieving rigorous convergence guarantees and an end-to-end bound on sampling error that shows complexity independent of isoperimetric conditions under accurate score knowledge.
We introduce a novel alignment method for diffusion models from distribution optimization perspectives while providing rigorous convergence guarantees. We first formulate the problem as a generic regularized loss minimization over probability distributions and directly optimize the distribution using the Dual Averaging method. Next, we enable sampling from the learned distribution by approximating its score function via Doob's $h$-transform technique. The proposed framework is supported by rigorous convergence guarantees and an end-to-end bound on the sampling error, which imply that when the original distribution's score is known accurately, the complexity of sampling from shifted distributions is independent of isoperimetric conditions. This framework is broadly applicable to general distribution optimization problems, including alignment tasks in Reinforcement Learning with Human Feedback (RLHF), Direct Preference Optimization (DPO), and Kahneman-Tversky Optimization (KTO). We empirically validate its performance on synthetic and image datasets using the DPO objective.