# Theoretical guidelines for annealed Langevin dynamics in compositional simulation-based inference

arXiv: https://arxiv.org/abs/2605.21253 · HTML: https://mlsanity.com/paper/2605.21253/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 29 references that are in the map.
- First posted on arXiv 20 May 2026.

## Builds on (most cited first, 22 of 22)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1507.05021/) (2015)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient](https://mlsanity.com/paper/1710.00095/) (2017)
- [Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models](https://mlsanity.com/paper/2210.04872/) (2022)
- [Compositional Score Modeling for Simulation-based Inference](https://mlsanity.com/paper/2209.14249/) (2022)
- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [The Tamed Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1710.05559/) (2017)
- [Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distance](https://mlsanity.com/paper/2501.02298/) (2025)
- [HNPE: Leveraging Global Parameters for Neural Posterior Estimation](https://mlsanity.com/paper/2102.06477/) (2021)
- [Diffusion posterior sampling for simulation-based inference in tall data settings](https://mlsanity.com/paper/2404.07593/) (2024)
- [Gaussian Interpolation Flows](https://mlsanity.com/paper/2311.11475/) (2023)
- [Compositional simulation-based inference for time series](https://mlsanity.com/paper/2411.02728/) (2024)
- [Error analysis of a compositional score-based algorithm for simulation-based inference](https://mlsanity.com/paper/2510.15817/) (2025)

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

- [Scalable Diffusion SBI for Compositional Inference under Simulator Misspecification](https://mlsanity.com/paper/2609.36950/) (2026)

## Abstract (arXiv)

Compositional score-based approaches to simulation-based inference (SBI) approximate the posterior over a shared parameter given n independent observations by aggregating individually learned posterior scores: currently, there are two main propositions of such methods (Geffner et al. (2023), Linhart et al. (2026)). As the resulting composite score does not correspond to the score of any distribution along the forward diffusion path of the true multi-observation posterior, sampling from it via a reverse SDE leads to an irreducible bias. Annealed Langevin dynamics provides a principled alternative: it treats the composite score as the genuine score of a sequence of tractable bridging densities and samples from them in succession. When properly tuned, it could lead to a controllable bias. However, its hyperparameters, namely step sizes, the number of steps per level, and the number of annealing levels, have so far been chosen empirically. We derive Wasserstein bounds for annealed Langevin with approximate scores and translate them into explicit decision rules for these hyperparameters that guarantee a prescribed sampling accuracy, while highlighting different theoretical aspects of each composite score formulation. In the Gaussian setting, we obtain closed-form expressions for all relevant quantities and prove that the bridging densities of Linhart et al. (2026) consistently admit larger step sizes and require fewer total Langevin steps than those of Geffner et al. (2023). Furthermore, we show empirically that the tuning obtained in the Gaussian setting generalizes to more complex problems, thus providing a well-understood and theoretically grounded starting point for practitioners using compositional score-based approaches.