Riemannian Continuous Normalizing Flows
arXiv:2006.10605
Abstract
Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, torii, and hyperbolic spaces, most normalizing flows implicitly assume a flat geometry, making them either misspecified or ill-suited in these situations. To overcome this problem, we introduce Riemannian continuous normalizing flows, a model which admits the parametrization of flexible probability measures on smooth manifolds by defining flows as the solution to ordinary differential equations. We show that this approach can lead to substantial improvements on both synthetic and real-world data when compared to standard flows or previously introduced projected flows.
arXiv commentcamera ready NeurIPS 2020
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Cited by in corpus (13)
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- Hyperbolic Busemann Learning with Ideal Prototypes
- Continuous-Depth Neural Models for Dynamic Graph Prediction
- Second-Order Neural ODE Optimizer
- Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flows
- Spherical Sliced-Wasserstein
- Equivariant Manifold Flows
- Continuous normalizing flows on manifolds
- Implicit Riemannian Concave Potential Maps