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Riemannian Diffusion Models
Chin-Wei Huang · Milad Aghajohari · Joey Bose · Prakash Panangaden · Aaron Courville

Thu Dec 01 02:00 PM -- 04:00 PM (PST) @ Hall J #331

Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for likelihood estimation. Computationally, we propose new methods for computing the Riemannian divergence which is needed for likelihood estimation. Moreover, in generalizing the Euclidean case, we prove that maximizing this variational lower-bound is equivalent to Riemannian score matching. Empirically, we demonstrate the expressive power of Riemannian diffusion models on a wide spectrum of smooth manifolds, such as spheres, tori, hyperboloids, and orthogonal groups. Our proposed method achieves new state-of-the-art likelihoods on all benchmarks.

Author Information

Chin-Wei Huang (Microsoft Research)
Milad Aghajohari (Montreal Institute for Learning Algorithms, University of Montreal, Université de Montréal)
Joey Bose (McGill/MILA)

I’m a PhD student at the RLLab at McGill/MILA where I work on Adversarial Machine Learning on Graphs. Previously, I was a Master’s student at the University of Toronto where I researched crafting Adversarial Attacks on Computer Vision models using GAN’s. I also interned at Borealis AI where I was working on applying adversarial learning principles to learn better embeddings i.e. Word Embeddings for Machine Learning models.

Prakash Panangaden (McGill University, Montreal)
Aaron Courville (Mila, U. Montreal)

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