Efficient Multimodal Sampling via Tempered Distribution Flow

Sampling from high-dimensional distributions is a fundamental problem in statistical research and practice. However, great challenges emerge when the target density function unnormalized contains isolated modes. We tackle this difficulty by fitting an invertible transformation mapping, called transport map, between reference probability measure distribution, so that sampling distribution can be achieved pushing forward sample through map. theoretically analyze limitations of existing transport-based methods using Wasserstein gradient flow theory, propose new method TemperFlow addresses multimodality issue. adaptively learns sequence tempered to progressively approach we prove it overcomes methods. Various experiments demonstrate superior performance novel sampler compared traditional methods, show its applications modern deep learning tasks such as image generation. The programming code for numerical available supplementary material.