Abstract
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.
Abstract (translated)
生成模型已经作为解决逆向问题的强大先验条件而出现。这些模型通常使用单一固定的复杂度或维度来表示一类自然信号。然而，这可能具有局限性：根据具体的问题，固定不变的复杂度可能会导致在复杂度过低时产生高代表误差，或者在复杂度过高时过度拟合噪声。我们开发了可调复杂度先验条件用于扩散模型、归一化流和变分自编码器，并利用嵌套 dropout 技术实现。在包括压缩感知、图像修复、去噪以及相位检索在内的多项任务中，实验结果表明，可调的先验条件始终比固定复杂度的基础模型获得更低的重建误差。 在线性去噪设定下，我们提供了理论分析，明确说明了最优调整参数如何依赖于噪声水平和模型结构。这项工作展示了可调复杂度生成先验的巨大潜力，并激发了开发支持理论以及将其应用于广泛逆向问题的研究动力。
URL
https://arxiv.org/abs/2603.07357
