VQ-Flows: Vector Quantized Local Normalizing Flows
This addresses a bottleneck in generative modeling for researchers and practitioners working with complex data distributions, though it is incremental as it builds on existing normalizing flow and VQ-AE techniques.
The authors tackled the problem of limited expressivity in normalizing flows for data on low-dimensional manifolds or with non-trivial topology by introducing VQ-Flows, a mixture of local normalizing flows as chart maps, which preserves exact density evaluation and improves modeling of complex manifolds in experiments.
Normalizing flows provide an elegant approach to generative modeling that allows for efficient sampling and exact density evaluation of unknown data distributions. However, current techniques have significant limitations in their expressivity when the data distribution is supported on a low-dimensional manifold or has a non-trivial topology. We introduce a novel statistical framework for learning a mixture of local normalizing flows as "chart maps" over the data manifold. Our framework augments the expressivity of recent approaches while preserving the signature property of normalizing flows, that they admit exact density evaluation. We learn a suitable atlas of charts for the data manifold via a vector quantized auto-encoder (VQ-AE) and the distributions over them using a conditional flow. We validate experimentally that our probabilistic framework enables existing approaches to better model data distributions over complex manifolds.