Riemannian Score-Based Generative Modeling

Bortoli, Valentin De; Mathieu, Émile; Hutchinson, Michael; Thornton, Jim; Teh, Yee Whye; Doucet, Arnaud

doi:10.48550/arxiv.2202.02763

Cited by 9 publications

(12 citation statements)

References 63 publications

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“…Sampling remains slower than normal EBMs due to the complexity of constrained Langevin dynamics steps. Constrained EBMs might thus be better scaled by training methods that do not require sampling, such as learning the Stein discrepancy [34] or score-based techniques [21,78].…”

Section: Discussionmentioning

confidence: 99%

“…Constrained energy-based models on neural implicit manifolds represent a novel method which we hope can be scaled up in the future to datasets with high-dimensional manifold structure such as images. For this experiment section, we note that density estimation on manifolds even of few dimensions is of interest in the literature [21,29,54,70]. Such models are typically bespoke: constructed using known geometric properties of the manifold.…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Neural Implicit Manifold Learning for Topology-Aware Generative Modelling

Ross¹,

Loaiza-Ganem²,

Caterini³

et al. 2022

Preprint

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Natural data observed in R n is often constrained to an m-dimensional manifold M, where m < n. Current generative models represent this manifold by mapping an m-dimensional latent variable through a neural network f θ : R m → R n . Such procedures, which we call pushforward models, incur a straightforward limitation: manifolds cannot in general be represented with a single parameterization, meaning that attempts to do so will incur either computational instability or the inability to learn probability densities within the manifold. To remedy this problem, we propose to model M as a neural implicit manifold: the set of zeros of a neural network. To learn the data distribution within M, we introduce constrained energybased models, which use a constrained variant of Langevin dynamics to train and sample within a learned manifold. The resulting model can be manipulated with an arithmetic of manifolds which allows practitioners to take unions and intersections of model manifolds. In experiments on synthetic and natural data, we show that constrained EBMs can learn manifold-supported distributions with complex topologies more accurately than pushforward models.Preprint. Under review.

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Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Neural Implicit Manifold Learning for Topology-Aware Generative Modelling

Ross¹,

Loaiza-Ganem²,

Caterini³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Atoms in a molecule do not have natural orientations, so the generation process differs from generating protein structures. Diffusion models have also been extended to non-Euclidean data, such as data in the Riemannian manifolds [Leach et al, 2022, De Bortoli et al, 2022]. These models are relevant to modeling orientations which are represented by elements in SO(3).…”

Section: Related Workmentioning

confidence: 99%

Antigen-Specific Antibody Design and Optimization with Diffusion-Based Generative Models for Protein Structures

Luo

Peng

et al. 2022

Preprint

103

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Antibodies are immune system proteins that protect the host by binding to specific antigens such as viruses and bacteria. The binding between antibodies and antigens are mainly determined by the complementarity-determining regions (CDR) on the antibodies. In this work, we develop a deep generative model that jointly models sequences and structures of CDRs based on diffusion processes and equivariant neural networks. Our method is the first deep learning-based method that can explicitly target specific antigen structures and generate antibodies at atomic resolution. The model is a ''Swiss Army Knife'' which is capable of sequence-structure co-design, sequence design for given backbone structures, and antibody optimization. For antibody optimization, we propose a special sampling scheme that first perturbs the given antibody and then denoises it. As the number of available antibody structures is relatively scarce, we curate a new dataset that contains antibody-like proteins as a complement to the original antibody dataset for training. We conduct extensive experiments to evaluate the quality of both sequences and structures of designed antibodies. We find that our model could yield highly competitive results in terms of binding affinity measured by biophysical energy functions and other protein design metrics.

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“…shape generation [4,51,85], video generation [26,83], Riemannian manifolds [16], symbolic music generation [54], guided image synthesis [52] and text-to-image [59]. In contrast to these works, our main focus is not to improve empirical results on existing diffusion models, analyse their behaviour or extend them to new data domains.…”

Section: Related Workmentioning

confidence: 99%

Generative Modelling With Inverse Heat Dissipation

Rissanen¹,

Heinonen²,

Solin³

2022

Preprint

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While diffusion models have shown great success in image generation, their noiseinverting generative process does not explicitly consider the structure of images, such as their inherent multi-scale nature. Inspired by diffusion models and the desirability of coarse-to-fine modelling, we propose a new model that generates images through iteratively inverting the heat equation, a PDE that locally erases fine-scale information when run over the 2D plane of the image. In our novel methodology, the solution of the forward heat equation is interpreted as a variational approximation in a directed graphical model. We demonstrate promising image quality and point out emergent qualitative properties not seen in diffusion models, such as disentanglement of overall colour and shape in images and aspects of neural network interpretability. Spectral analysis on natural images positions our model as a type of dual to diffusion models and reveals implicit inductive biases in them.Preprint. Under review.

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Riemannian Score-Based Generative Modeling

Cited by 9 publications

References 63 publications

Neural Implicit Manifold Learning for Topology-Aware Generative Modelling

Neural Implicit Manifold Learning for Topology-Aware Generative Modelling

Antigen-Specific Antibody Design and Optimization with Diffusion-Based Generative Models for Protein Structures

Generative Modelling With Inverse Heat Dissipation

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