# Geodesic Slice Sampler for Multimodal Distributions with Strong Curvature

arXiv: https://arxiv.org/abs/2502.21190 · HTML: https://mlsanity.com/paper/2502.21190/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 39 references that are in the map.
- First posted on arXiv 28 Feb 2025.

## Builds on (most cited first, 12 of 12)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [BlackJAX: Composable Bayesian inference in JAX](https://mlsanity.com/paper/2402.10797/) (2024)
- [Diffusive Gibbs Sampling](https://mlsanity.com/paper/2402.03008/) (2024)
- [Lagrangian Manifold Monte Carlo on Monge Patches](https://mlsanity.com/paper/2202.00755/) (2022)
- [Markovian Flow Matching: Accelerating MCMC with Continuous Normalizing Flows](https://mlsanity.com/paper/2405.14392/) (2024)
- [Riemannian Laplace Approximation with the Fisher Metric](https://mlsanity.com/paper/2311.02766/) (2023)
- [Convergence of hybrid slice sampling via spectral gap](https://mlsanity.com/paper/1409.2709/) (2014)
- [Geodesic slice sampling on the sphere](https://mlsanity.com/paper/2301.08056/) (2023)
- [Warped geometric information on the optimisation of Euclidean functions](https://mlsanity.com/paper/2308.08305/) (2023)

## Built on by (most cited first, 2 of 2)

- [Reducing Memorisation in Generative Models via Riemannian Bayesian Inference](https://mlsanity.com/paper/2602.00199/) (2026)
- [Disentanglement Beyond Generative Models with Riemannian ICA](https://mlsanity.com/paper/2605.22531/) (2026)

## Abstract (arXiv)

Traditional Markov Chain Monte Carlo sampling methods often struggle with sharp curvatures, intricate geometries, and multimodal distributions. Slice sampling can resolve local exploration inefficiency issues, and Riemannian geometries help with sharp curvatures. Recent extensions enable slice sampling on Riemannian manifolds, but they are restricted to cases where geodesics are available in a closed form. We propose a method that generalizes Hit-and-Run slice sampling to more general geometries tailored to the target distribution, by approximating geodesics as solutions to differential equations. Our approach enables the exploration of the regions with strong curvature and rapid transitions between modes in multimodal distributions. We demonstrate the advantages of the approach over challenging sampling problems.