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arXiv Machine Learning

Tunable Latent Generative Priors for Compressed Sensing and Inverse Problems

The paper introduces tunable latent priors for diffusion models, normalizing flows, and variational autoencoders using nested dropout. These priors allow the latent dimensionality to adapt to each inverse problem, reducing reconstruction errors compared to fixed-complexity models across tasks such as compressed sensing, inpainting, denoising, and phase retrieval. In linear denoising, the authors derive the optimal latent complexity in closed form, linking it to noise level and signal spectrum.

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arXiv Machine Learning
Sep 3

Full-Model Optimality for Tunable Linear Generative Priors in Compressed Sensing

The paper investigates compressed sensing using a family of tunable linear generative priors linked through their singular value decompositions. It proves that in noiseless Gaussian compressed sensing, the full-dimensional linear prior yields the lowest expected reconstruction error across the entire family, meaning lower-complexity priors do not improve performance in this idealized setting. This contrasts with denoising, where lower complexity priors can reduce error due to bias‑variance tradeoffs, suggesting that the experimental gains seen with neural network priors stem from their nonlinearities.

By Zhaoming Li, Paul Hand
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arXiv Machine Learning
Oct 3

Trajectory Stitching for Solving Inverse Problems with Flow-Based Models

The paper introduces MS-Flow, a method that represents a flow-based generative model’s trajectory as a sequence of intermediate latent states instead of a single initial code. By enforcing local flow dynamics and coupling trajectory segments with matching penalties, the approach alternates between updating latent states and ensuring consistency with observed data. This strategy reduces memory usage and improves reconstruction quality on tasks such as image inpainting, super‑resolution, and computed tomography.

By Alexander Denker, Zeljko Kereta, Carola-Bibiane Sch\"onlieb, Moshe Eliasof
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arXiv Machine Learning
Sep 2

HarmoCore: Functional Latent Diffusion for Sparse Reconstruction of Oscillatory Wave Fields

HarmoCore introduces a generative prior in a compact, continuous latent space for reconstructing oscillatory wave fields from extremely sparse sensor data. It models joint real–imaginary channels using Functional Tucker cores over shared spatial bases, learns a frequency‑conditioned diffusion prior, and performs diffusion posterior sampling directly in core space. Experiments on 2D and 3D Helmholtz problems demonstrate significant performance gains with only 1%–2% sensor coverage while remaining scalable to three dimensions.

By Lihao Chen, Xinyu Zhang, Panqi Chen, Lei Cheng, Ting Zhang, Jianlong Li, Shikai Fang
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arXiv Statistics ML
Oct 28

Latent Nonlinear Denoising Score Matching for Enhanced Learning of Structured Distributions

The paper introduces Latent Nonlinear Denoising Score Matching (LNDSM), a method that integrates nonlinear, structure-informed latent diffusions with a variational autoencoder framework. LNDSM designs the forward diffusion to admit a chosen reference distribution, such as a Gaussian mixture, and derives a computable approximation to a cross‑entropy upper bound using Euler‑Maruyama discretization. Experiments on benchmark image datasets show that LNDSM improves sample quality, mode balance, and training efficiency compared to conventional latent score‑based generative models.

By Kaichen Shen, Wei Zhu
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