# Conditional Diffusion Sampling

arXiv: https://arxiv.org/abs/2605.04013 · HTML: https://mlsanity.com/paper/2605.04013/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 19 of its 55 references that are in the map.
- First posted on arXiv 5 May 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 19 of 19)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)
- [Flow Annealed Importance Sampling Bootstrap](https://mlsanity.com/paper/2208.01893/) (2022)
- [Iterated Denoising Energy Matching for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2402.06121/) (2024)
- [Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2102.07501/) (2021)
- [Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matching](https://mlsanity.com/paper/2504.11713/) (2025)
- [NETS: A Non-Equilibrium Transport Sampler](https://mlsanity.com/paper/2410.02711/) (2024)
- [Reverse Diffusion Monte Carlo](https://mlsanity.com/paper/2307.02037/) (2023)
- [No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplers](https://mlsanity.com/paper/2502.06685/) (2025)
- [Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2506.16471/) (2025)
- [Transport meets Variational Inference: Controlled Monte Carlo Diffusions](https://mlsanity.com/paper/2307.01050/) (2023)
- [Diffusive Gibbs Sampling](https://mlsanity.com/paper/2402.03008/) (2024)
- [Training Neural Samplers with Reverse Diffusive KL Divergence](https://mlsanity.com/paper/2410.12456/) (2024)
- [Accelerated Parallel Tempering via Neural Transports](https://mlsanity.com/paper/2502.10328/) (2025)
- [Progressive Tempering Sampler with Diffusion](https://mlsanity.com/paper/2506.05231/) (2025)

## Built on by (most cited first, 1 of 1)

- [Mode Collapse Is Cheap to Detect: A Ground-Truth-Free Pre-Flight Check for Neural Samplers](https://mlsanity.com/paper/2609.26272/) (2026)

## Abstract (arXiv)

Sampling from unnormalized multimodal distributions with limited density evaluations remains a fundamental challenge in machine learning and natural sciences. Successful approaches construct a bridge between a tractable reference and the target distribution. Parallel Tempering (PT) serves as the gold standard, while recent diffusion-based approaches offer a continuous alternative at the cost of neural training. In this work, we introduce Conditional Diffusion Sampling (CDS), a framework that combines these two paradigms. To this end, we derive Conditional Interpolants, a class of stochastic processes whose transport dynamics are governed by an exact, closed-form stochastic differential equation (SDE), requiring no neural approximation. Although these dynamics require sampling from a non-trivial initialization distribution, we show both theoretically and empirically that the cost of this initialization diminishes for sufficiently short diffusion times. CDS leverages this by a two-stage procedure: (1) PT is used to efficiently sample the initial distribution, and then (2) samples are transported via the transport SDE. This combination couples the robust global exploration of PT with efficient local transport. Experiments suggest that CDS has the potential to achieve a superior trade-off between sample quality and density evaluation cost compared to state-of-the-art samplers.