# Riemannian Score-Based Generative Modeling

@article{Bortoli2022RiemannianSG, title={Riemannian Score-Based Generative Modeling}, author={Valentin De Bortoli and Emile Mathieu and Michael Hutchinson and James Thornton and Yee Whye Teh and A. Doucet}, journal={ArXiv}, year={2022}, volume={abs/2202.02763} }

Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a “noising” stage, whereby a diffusion is used to gradually add Gaussian noise to data, and a generative model, which entails a “denoising” process deﬁned by approximating the time-reversal of the diffusion. Existing SGMs assume that data is supported on a Euclidean space, i.e. a manifold with ﬂat geometry. In many…

## 11 Citations

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A general framework is proposed which not only unifies and generalizes this approach to a wide class of spaces but also leads to an original extension of score matching.

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A diverse range of advanced techniques to speed up the diffusion models – training schedule, training-free sampling, mixed-modeling, and score & diffusion uniﬁcation are presented.

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This paper presents a stochastic differential equation (SDE) approach for general-purpose image restoration that transforms a high-quality image into a degraded counterpart as a mean state with Gaussian noise and proposes a maximum likelihood objective to learn an optimal reverse trajectory which stabilizes the training and improves the restoration results.

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By fine tuning the RoseTTAFold structure prediction network on protein structure denoising tasks, this work obtains a generative model of protein backbones that achieves outstanding performance on unconditional and topology-constrained protein monomers design, protein binder design, symmetric oligomer design, enzyme active site scaffolding, and symmetric motif scaffolding for therapeutic and metal-binding protein design.

### Denoising Deep Generative Models

- Computer ScienceArXiv
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This paper proposes two methodologies based on adding Gaussian noise to the data to remove the dimensionality mismatch during training, and both provide a denoising mechanism whose goal is to sample from the model as though no noise had been added to theData.

### Diffusion Generative Models in Infinite Dimensions

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This work generalizes diffusion models to operate directly in function space by developing the foundational theory for such models in terms of Gaussian measures on Hilbert spaces and developing methods for diffusion generative modeling in Sobolev spaces.

### The Union of Manifolds Hypothesis

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