Riemannian Metric Matching: amortized diffusion geometry up to 400x faster (ICML Oral)

allen_ai · x · 2026-09-16

An ICML 2026 Oral from Jacob Bamberger, Adam Gosztolai and Michael Bronstein et al. proposes Riemannian Metric Matching: a denoising probabilistic framework that learns the Riemannian geometry of data with neural networks. Key insight: the carré du champ operator is a conditional expectation over random perturbations, enabling sample-wise training and constant-cost amortized inference without kernel construction. It rivals or beats kNN-based diffusion geometry estimators, with inference up to 400x faster, and supports graph-free geometric analysis on high-dimensional images. Code, pretrained models and tutorial notebooks are released.

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