# Scalable Simulation-Based Model Inference with Test-Time Complexity Control

arXiv: https://arxiv.org/abs/2603.15292 · HTML: https://mlsanity.com/paper/2603.15292/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 97 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Builds on (most cited first, 30 of 34)

- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017)
- [Real-time gravitational-wave science with neural posterior estimation](https://mlsanity.com/paper/2106.12594/) (2021)
- [All-in-one simulation-based inference](https://mlsanity.com/paper/2404.09636/) (2024)
- [Simulation Intelligence: Towards a New Generation of Scientific Methods](https://mlsanity.com/paper/2112.03235/) (2021)
- [Bayesian Model Selection, the Marginal Likelihood, and Generalization](https://mlsanity.com/paper/2202.11678/) (2022)
- [Bayesian Workflow](https://mlsanity.com/paper/2011.01808/) (2020)
- [Investigating the Impact of Model Misspecification in Neural Simulation-based Inference](https://mlsanity.com/paper/2209.01845/) (2022)
- [JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models](https://mlsanity.com/paper/2302.09125/) (2023)
- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [Can Transformers Learn Full Bayesian Inference in Context?](https://mlsanity.com/paper/2501.16825/) (2025)
- [Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inference](https://mlsanity.com/paper/2210.05686/) (2022)
- [sbi reloaded: a toolkit for simulation-based inference workflows](https://mlsanity.com/paper/2411.17337/) (2024)
- [Amortized Bayesian model comparison with evidential deep learning](https://mlsanity.com/paper/2004.10629/) (2020)
- [A Deep Learning Method for Comparing Bayesian Hierarchical Models](https://mlsanity.com/paper/2301.11873/) (2023)
- [Informed Equation Learning](https://mlsanity.com/paper/2105.06331/) (2021)
- [Evidence Networks: simple losses for fast, amortized, neural Bayesian model comparison](https://mlsanity.com/paper/2305.11241/) (2023)
- [Simulation-based Bayesian inference under model misspecification](https://mlsanity.com/paper/2503.12315/) (2025)
- [Simultaneous identification of models and parameters of scientific simulators](https://mlsanity.com/paper/2305.15174/) (2023)

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

- [Mixed neural posterior estimation for simulators with discrete and continuous parameters](https://mlsanity.com/paper/2605.13551/) (2026)
- [LinearPFN: Amortized Variable Selection for Linear Models with Interactions](https://mlsanity.com/paper/2610.06580/) (2026)

## Abstract (arXiv)

Simulation plays a central role in scientific discovery. In many applications, the bottleneck is no longer running a simulator; it is choosing among large families of plausible simulators, each corresponding to different forward models/hypotheses consistent with observations. Over large model families, classical Bayesian workflows for model selection are impractical. Furthermore, amortized model selection methods typically hard-code a fixed model prior or complexity penalty at training time, requiring users to commit to a particular parsimony assumption before seeing the data. We introduce PRISM, a simulation-based encoder-decoder that infers a joint posterior over both discrete model structures and associated continuous parameters, while enabling test-time control of model complexity via a tunable model prior that the network is conditioned on. We show that PRISM scales to families with combinatorially many (up to billions) of model instantiations on a synthetic symbolic regression task. As a scientific application, we evaluate PRISM on biophysical modeling for diffusion MRI data, showing the ability to perform model selection across several multi-compartment models, on both synthetic and in vivo neuroimaging data.