Linear Multistep Solver Distillation for Fast Sampling of Diffusion Models
Yuchen Liang Xiangzhong Fang Hanting Chen Yunhe Wang
Sampling from diffusion models can be seen as solving the corresponding 
   probability flow ordinary differential equation (ODE). 
   The solving process requires a significant number of function 
   evaluations (NFE), making it time-consuming. 
   Recently, several solver search frameworks have attempted to find 
   better-performing model-specific solvers. However, predicting the impact of 
   intermediate solving strategies on final sample quality remains challenging, 
   rendering the search process inefficient.
   In this paper, we propose a novel method for designing 
   solving strategies. We first introduce a unified prediction formula 
   for linear multistep solvers. Subsequently, we present a solver distillation 
   framework, which enables a student solver to mimic the sampling trajectory 
   generated by a teacher solver with more steps. We utilize the mean Euclidean 
   distance between the student and teacher sampling trajectories as a metric, 
   facilitating rapid adjustment and optimization of intermediate solving strategies.
   The design space of our framework encompasses multiple aspects, 
   including prediction coefficients, time step schedules, and time scaling 
   factors. 
   Our framework has the ability to complete a solver search 
   for Stable-Diffusion in under 12 total GPU hours.
   Compared to previous reinforcement learning-based 
   search frameworks, 
   our approach achieves over a 10$\times$ increase in search efficiency. 
   With just 5 NFE, we achieve FID scores of 3.23 on CIFAR10, 7.16 on ImageNet-64, 
   5.44 on LSUN-Bedroom, and 12.52 on MS-COCO, resulting in a 2$\times$ sampling acceleration ratio 
   compared to handcrafted solvers.
Diffusion Probabilistic Model, Diffusion Sampler, Solver Schedule
We provide a solver distillation  framework for diffusion models and search for solver schedules based on it.