Deep Probabilistic Priors for Solving Inverse Problems
Paweł A. Pierzchlewicz · 2025
Inverse problems are problems where causal sources are inferred from observed effects. They are ubiquitous in science and engineering. Examples include image reconstruction from neural responses, feature visualizations of a deep neural network and 3D pose estimation from 2D images. These problems are inherently ill-posed, often having multiple solutions for a given set of observations. The standard approach to solve inverse problems is to use simplified hand-crafted priors, which struggle with high-dimensional data that lies on very constrained manifolds such as images or human poses. This thesis studies the application of deep probabilistic priors to solve inverse problems more effectively. I explore the idea that deep probabilistic priors, such as Normalizing Flows and Diffusion Models, could improve the quality and robustness of solutions compared to traditional methods. I tested this hypothesis in two domains: vision neuroscience and human pose estimation. In the domain of neuroscience, I showed that using a diffusion model helps instill a better natural image prior, thus improving architecture generalizability in the tasks of synthesizing most exciting inputs for individual neurons and reconstructing images from neural responses. I compared the deep probabilistic prior to previous state-of-the-art handcrafted regularization methods on each of these tasks. In the domain of human pose estimation, I first showed that existing multi-hypothesis pose estimation methods are miscalibrated. By using a deep probabilistic prior in the form of a normalizing flow and then improving upon it with a diffusion model, I showed that the issue of calibration can be mitigated when optimizing for likelihood based objectives rather than sample based metrics. Furthermore, I explored the zero-shot capabilities of this approach, showing that with a deep probabilistic prior we can zero-shot infer new human motions. Through a series of experiments and case studies, I demonstrate that deep probabilistic priors for inverse problems outperform hand-crafted regularization techniques in terms of accuracy, robustness, and calibration. My findings suggest that deep probabilistic priors offer a promising avenue for tackling complex inverse problems across various domains.