Wasserstein Gradient Flows and Forward-Only Diffusion Are Not Enough for Multimodal Sampling
The paper argues the bottleneck is structural: local gradient transport can take exponentially long to move mass between separated modes.
The authors say Wasserstein gradient-flow samplers and overdamped forward diffusion share the same density evolution, so both inherit metastability and slow mixing. Their spectral and mean first-passage analyses tie well-separated modes to small spectral gaps and rare transitions. For the log-linear annealing schedule they study, intermediate distributions still do not remove the exponential transport-time scaling. ArXiv · AI/CL/LG's note
The authors say Wasserstein gradient-flow samplers and overdamped forward diffusion share the same density evolution, so both inherit metastability and slow mixing. Their spectral and mean first-passage analyses tie well-separated modes to small spectral gaps and rare transitions. For the log-linear annealing schedule they study, intermediate distributions still do not remove the exponential transport-time scaling. ArXiv · AI/CL/LG's note
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