Diffusion Generative Models Meet Compressed Sensing, with Applications to Imaging and Finance
This work addresses efficiency bottlenecks in diffusion models for applications in imaging and finance, representing an incremental improvement with domain-specific impact.
The study tackled the problem of slow diffusion model inference by integrating compressed sensing to accelerate synthetic data generation, achieving provably faster convergence under sparsity assumptions and demonstrating effectiveness across datasets like handwritten digits, medical images, and financial time series.
In this study we develop dimension-reduction techniques to accelerate diffusion model inference in the context of synthetic data generation. The idea is to integrate compressed sensing into diffusion models (hence, CSDM): First, compress the dataset into a latent space (from an ambient space), and train a diffusion model in the latent space; next, apply a compressed sensing algorithm to the samples generated in the latent space for decoding back to the original space; and the goal is to facilitate the efficiency of both model training and inference. Under certain sparsity assumptions on data, our proposed approach achieves provably faster convergence, via combining diffusion model inference with sparse recovery. It also sheds light on the best choice of the latent space dimension. To illustrate the effectiveness of this approach, we run numerical experiments on a range of datasets, including handwritten digits, medical and climate images, and financial time series for stress testing.