arXiv AI By Runyu Zhang, Jiawei Zhang, Gioele Zardini, Saurabh Amin, Asuman Ozdaglar

Denoising as Projection: Constrained Optimization with Gradient-Guided Diffusion

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arXiv Machine Learning
Aug 31

Diffusion models as plug-and-play priors

The paper explores using denoising diffusion generative models as plug‑and‑play priors for high‑dimensional inference problems. By combining a pre‑trained diffusion prior with a differentiable auxiliary constraint, the authors enable approximate inference through iterative differentiation across multiple noisy versions of the data. This framework opens possibilities for conditional generation, image segmentation, and novel combinatorial optimization algorithms.

By Alexandros Graikos, Esmeralda S. Whitammer, Nebojsa Jojic, Dimitris Samaras
arXiv Machine Learning
Sep 14

Deep learning methods for inverse problems using connections between proximal operators and Hamilton-Jacobi equations

The paper proposes a deep learning framework that learns priors for inverse problems by exploiting the relationship between proximal operators and Hamilton–Jacobi partial differential equations. Unlike existing methods that require inverting the prior after training, this approach learns the prior directly, enabling efficient evaluation in a single forward pass. Numerical experiments demonstrate the method’s effectiveness in dimensions up to 64.

By Oluwatosin Akande, Gabriel P. Langlois, Akwum Onwunta