Diffusion Generative Models Meet Compressed Sensing, with Applications to Imaging and Finance

• URL: http://arxiv.org/abs/2509.03898v2
• Date: Sun, 28 Sep 2025 19:56:10 GMT
• Title: Diffusion Generative Models Meet Compressed Sensing, with Applications to Imaging and Finance
• Authors: Zhengyi Guo, Jiatu Li, Wenpin Tang, David D. Yao,
• Abstract summary: CSDM: First, compress the dataset into a latent 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.<n>Under certain sparsity assumptions on data, our proposed approach achieves provably faster convergence, via combining diffusion model inference with sparse recovery.<n>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.
• Score: 7.967038299436285
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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