Efficient Multimodal Sampling via Tempered Distribution Flow
This addresses a fundamental problem in statistical sampling for researchers and practitioners, though it appears incremental as it builds on existing transport-based methods.
The paper tackles the challenge of sampling from high-dimensional, multimodal distributions by proposing TemperFlow, a method that learns a sequence of tempered distributions to approach the target, and demonstrates superior performance in experiments and applications like image generation.
Sampling from high-dimensional distributions is a fundamental problem in statistical research and practice. However, great challenges emerge when the target density function is unnormalized and contains isolated modes. We tackle this difficulty by fitting an invertible transformation mapping, called a transport map, between a reference probability measure and the target distribution, so that sampling from the target distribution can be achieved by pushing forward a reference sample through the transport map. We theoretically analyze the limitations of existing transport-based sampling methods using the Wasserstein gradient flow theory, and propose a new method called TemperFlow that addresses the multimodality issue. TemperFlow adaptively learns a sequence of tempered distributions to progressively approach the target distribution, and we prove that it overcomes the limitations of existing methods. Various experiments demonstrate the superior performance of this novel sampler compared to traditional methods, and we show its applications in modern deep learning tasks such as image generation. The programming code for the numerical experiments is available at https://github.com/yixuan/temperflow.