# Scalable Diffusion SBI for Compositional Inference under Simulator Misspecification

arXiv: https://arxiv.org/abs/2609.36950 · HTML: https://mlsanity.com/paper/2609.36950/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 79 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 15 of 15)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Aligning Text-to-Image Diffusion Models with Reward Backpropagation](https://mlsanity.com/paper/2310.03739/) (2023)
- [Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Control](https://mlsanity.com/paper/2402.15194/) (2024)
- [Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Review](https://mlsanity.com/paper/2407.13734/) (2024)
- [Investigating the Impact of Model Misspecification in Neural Simulation-based Inference](https://mlsanity.com/paper/2209.01845/) (2022)
- [Rethinking Aleatoric and Epistemic Uncertainty](https://mlsanity.com/paper/2412.20892/) (2024)
- [Diffusion posterior sampling for simulation-based inference in tall data settings](https://mlsanity.com/paper/2404.07593/) (2024)
- [Diffusion Models in Simulation-Based Inference: A Tutorial Review](https://mlsanity.com/paper/2512.20685/) (2025)
- [Calibrating Generative Models to Distributional Constraints](https://mlsanity.com/paper/2510.10020/) (2025)
- [Flow Matching Calibration for Simulation-Based Inference under Model Misspecification](https://mlsanity.com/paper/2509.23385/) (2025)
- [Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training](https://mlsanity.com/paper/2606.09949/) (2026)
- [Tokenised Flow Matching for Hierarchical Simulation Based Inference](https://mlsanity.com/paper/2604.20723/) (2026)
- [Theoretical guidelines for annealed Langevin dynamics in compositional simulation-based inference](https://mlsanity.com/paper/2605.21253/) (2026)
- [WTF?! Simulation-Free Reinforcement Learning with Wasserstein-Tilted Flow Maps](https://mlsanity.com/paper/2609.27033/) (2026)

## Abstract (arXiv)

Simulation-based inference is challenging when many heterogeneous observations must be composed, hierarchical latent structure must be preserved, and the simulator is misspecified relative to observed data. We develop sampling and fine-tuning methods for diffusion-based inference in design-conditional settings, where the same simulator is queried across different experimental conditions xi. We extend compositional score-based inference with a continuous-time diffusion coefficient that accounts for the number of observations, avoiding Jacobian and auxiliary-covariance corrections. We introduce Hierarchical Blockwise Diffusion Sampling (HBDS), which infers shared parameters and group-specific latent states using a single pretrained model, with the hierarchy specified only at sampling time. Together, these methods support variable observation sets and groupings without retraining. To address misspecification, we introduce path-regularized fine-tuning that adapts the learned likelihood to observations and transfers corrections to posterior inference. Using Girsanov's theorem, we quantify path divergence between pretrained and fine-tuned models across experimental designs and interpret it alongside predictive errors to distinguish candidate misspecification correction from unnecessary adaptation. We evaluate compositional sampling on exact-score Gaussian and Simple Likelihood, Complex Posterior benchmarks, HBDS with analytic and learned scores on a controlled hierarchical model, and fine-tuning and localization on a separate analytic model with known design-dependent discrepancy. Finally, we apply the framework to 940 measurements across four cell lines in a mechanistic Bone Morphogenetic Protein signaling model, where fine-tuning improves posterior-predictive accuracy relative to the pretrained model and shifts posterior marginals toward the least-squares reference while retaining spread.