Accelerating Diffusion via Compressed Sensing: Applications to Imaging and Finance

We integrate compressed sensing with diffusion models to accelerate synthetic data generation. Our pipeline, \emph{Compressed-Space Diffusion Modeling (CSDM)}, first projects data from the ambient space to a latent space and trains a diffusion model in that space, then apply a compressed sensing algorithm to the latent samples to decode them back to the original space, with the goal of improving the efficiency of both training and inference. Under certain sparsity assumptions on the data, our approach achieves provably faster convergence by combining diffusion inference with sparse recovery, and it sheds light on the choice of the latent-space dimension. To illustrate the effectiveness of this approach, we present experiments on medical imaging data and financial time series for stress testing.