Multimodal Sampling with Schrödinger-Föllmer Samplers and Temperatures
Published:Dec 30, 2025 03:37
•1 min read
•ArXiv
Analysis
This paper introduces a novel sampling method, Schrödinger-Föllmer samplers (SFS), for generating samples from complex distributions, particularly multimodal ones. It improves upon existing SFS methods by incorporating a temperature parameter, which is crucial for sampling from multimodal distributions. The paper also provides a more refined error analysis, leading to an improved convergence rate compared to previous work. The gradient-free nature and applicability to the unit interval are key advantages over Langevin samplers.
Key Takeaways
- •Introduces Schrödinger-Föllmer samplers (SFS) with temperature parameters for improved sampling.
- •High temperatures are crucial for sampling from multimodal distributions.
- •Achieves an enhanced convergence rate of order $\mathcal{O}(h)$ in the $L^2$-Wasserstein distance.
- •SFS is gradient-free and works in the unit interval, unlike Langevin samplers.
- •Numerical experiments show SFS outperforms Langevin samplers, especially for multimodal distributions.
Reference
“The paper claims an enhanced convergence rate of order $\mathcal{O}(h)$ in the $L^2$-Wasserstein distance, significantly improving the existing order-half convergence.”