让生成模型自由调节复杂度，提升逆问题重建精度
Latent Generative Models with Tunable Complexity for Compressed Sensing and other Inverse Problems
- 用嵌套丢弃法构建可调复杂度的生成先验
- 在压缩感知等任务中均低于固定复杂度基线误差
- 理论证明噪声与模型结构影响最优复杂度选择
生成模型已成为解决逆问题的强大先验。传统方法通常使用单一固定复杂度表示自然信号，这可能带来局限：复杂度过低时重构误差高，过高则易过拟合噪声。本文为扩散模型、归一化流和变分自编码器设计了可调复杂度先验，利用嵌套丢弃实现。在压缩感知、补全、去噪和相位恢复等任务中，实验表明可调先验始终优于固定复杂度基线。在线性去噪场景下，我们提供理论分析，明确刻画最优调参如何依赖于噪声水平与模型结构。本工作展示了可调复杂度生成先验的潜力，并推动相关理论发展及在各类逆问题中的应用。
原文摘要 · Abstract (English)
Generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals using a single fixed complexity or dimensionality. This can be limiting: depending on the problem, a fixed complexity may result in high representation error if too small, or overfitting to noise if too large. We develop tunable-complexity priors for diffusion models, normalizing flows, and variational autoencoders, leveraging nested dropout. Across tasks including compressed sensing, inpainting, denoising, and phase retrieval, we show empirically that tunable priors consistently achieve lower reconstruction errors than fixed-complexity baselines. In the linear denoising setting, we provide a theoretical analysis that explicitly characterizes how the optimal tuning parameter depends on noise and model structure. This work demonstrates the potential of tunable-complexity generative priors and motivates both the development of supporting theory and their application across a wide range of inverse problems.
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