将压缩感知融入扩散模型，加速图像与金融数据生成。
Diffusion Generative Models Meet Compressed Sensing, with Applications to Imaging and Finance
- 在潜在空间训练扩散模型，结合压缩感知实现高效采样。
- 在数据稀疏条件下，收敛速度显著提升，理论可证明。
- 适合需要快速生成高质量数据的医学、气候与金融领域。
本研究提出一种基于压缩感知的扩散模型（CSDM）方法，通过将数据压缩至潜在空间并在此空间训练扩散模型，再利用压缩感知算法从潜在空间解码回原始空间，从而加速模型训练与推理。在数据满足一定稀疏性假设的前提下，该方法可实现理论上的更快收敛。实验在手写数字、医学图像、气候图像及金融时间序列等多类数据集上验证了其有效性，尤其适用于压力测试场景。结果表明，该方法能有效控制潜在空间维度，并在保持生成质量的同时大幅提高效率。
原文摘要 · Abstract (English)
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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