Reverse Transition Kernel: A Flexible Framework to Accelerate Diffusion Inference

To generate data from trained diffusion models, most inference algorithms, such as DDPM, DDIM, and other variants, rely on discretizing the reverse SDEs or their equivalent ODEs. In this paper, we view such approaches as decomposing the entire denoising diffusion process into several segments, each corresponding to a reverse transition kernel (RTK) sampling subproblem. Specifically, DDPM uses a Gaussian approximation for the RTK, resulting in low per-subproblem complexity but requiring a large number of segments (i.e., subproblems), which is conjectured to be inefficient. To address this, we develop a general RTK framework that enables a more balanced subproblem decomposition, resulting in \tilde O(1) subproblems, each with strongly log-concave targets. We then propose leveraging two fast sampling algorithms, the Metropolis-Adjusted Langevin Algorithm (MALA) and Underdamped Langevin Dynamics (ULD), for solving these strongly log-concave subproblems.