# All-in-one simulation-based inference

arXiv: https://arxiv.org/abs/2404.09636 · HTML: https://mlsanity.com/paper/2404.09636/

## Key facts

- Cited by 74 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 77 references that are in the map.
- First posted on arXiv 15 Apr 2024.

## Builds on (most cited first, 30 of 52)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Flexible Diffusion Modeling of Long Videos](https://mlsanity.com/paper/2205.11495/) (2022)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [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)
- [Transformer Neural Processes: Uncertainty-Aware Meta Learning Via Sequence Modeling](https://mlsanity.com/paper/2207.04179/) (2022)
- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Sparse is Enough in Scaling Transformers](https://mlsanity.com/paper/2111.12763/) (2021)
- [Real-time gravitational-wave science with neural posterior estimation](https://mlsanity.com/paper/2106.12594/) (2021)
- [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)
- [Variational methods for simulation-based inference](https://mlsanity.com/paper/2203.04176/) (2022)
- [A Survey on Principles, Models and Methods for Learning from Irregularly Sampled Time Series](https://mlsanity.com/paper/2012.00168/) (2020)

## Built on by (most cited first, 30 of 74)

- [PaperBench: Evaluating AI's Ability to Replicate AI Research](https://mlsanity.com/paper/2504.01848/) (2025)
- [Do-PFN: In-Context Learning for Causal Effect Estimation](https://mlsanity.com/paper/2506.06039/) (2025)
- [Neural Methods for Amortized Inference](https://mlsanity.com/paper/2404.12484/) (2024)
- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [Amortized Probabilistic Conditioning for Optimization, Simulation and Inference](https://mlsanity.com/paper/2410.15320/) (2024)
- [sbi reloaded: a toolkit for simulation-based inference workflows](https://mlsanity.com/paper/2411.17337/) (2024)
- [Position: The Future of Bayesian Prediction Is Prior-Fitted](https://mlsanity.com/paper/2505.23947/) (2025)
- [Amortized Bayesian Multilevel Models](https://mlsanity.com/paper/2408.13230/) (2024)
- [Distribution Transformers: Fast Approximate Bayesian Inference With On-The-Fly Prior Adaptation](https://mlsanity.com/paper/2502.02463/) (2025)
- [Effortless, Simulation-Efficient Bayesian Inference using Tabular Foundation Models](https://mlsanity.com/paper/2504.17660/) (2025)
- [Solving Empirical Bayes via Transformers](https://mlsanity.com/paper/2502.09844/) (2025)
- [Does Unsupervised Domain Adaptation Improve the Robustness of Amortized Bayesian Inference? A Systematic Evaluation](https://mlsanity.com/paper/2502.04949/) (2025)
- [Compositional simulation-based inference for time series](https://mlsanity.com/paper/2411.02728/) (2024)
- [Multifidelity Simulation-based Inference for Computationally Expensive Simulators](https://mlsanity.com/paper/2502.08416/) (2025)
- [Simulation-based Bayesian inference under model misspecification](https://mlsanity.com/paper/2503.12315/) (2025)
- [FUSE: Fast Unified Simulation and Estimation for PDEs](https://mlsanity.com/paper/2405.14558/) (2024)
- [PABBO: Preferential Amortized Black-Box Optimization](https://mlsanity.com/paper/2503.00924/) (2025)
- [ALINE: Joint Amortization for Bayesian Inference and Active Data Acquisition](https://mlsanity.com/paper/2506.07259/) (2025)
- [A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference)](https://mlsanity.com/paper/2407.16550/) (2024)
- [Domain-Adaptive Neural Posterior Estimation for Strong Gravitational Lens Analysis](https://mlsanity.com/paper/2410.16347/) (2024)
- [Differentiable and Learnable Wireless Simulation with Geometric Transformers](https://mlsanity.com/paper/2406.14995/) (2024)
- [Simulation-based Inference with the Python Package sbijax](https://mlsanity.com/paper/2409.19435/) (2024)
- [Robust Simulation-Based Inference under Missing Data via Neural Processes](https://mlsanity.com/paper/2503.01287/) (2025)
- [Multilevel neural simulation-based inference](https://mlsanity.com/paper/2506.06087/) (2025)
- [Fast and Reliable Probabilistic Reflectometry Inversion with Prior-Amortized Neural Posterior Estimation](https://mlsanity.com/paper/2407.18648/) (2024)
- [Arbitrarily-Conditioned Multi-Functional Diffusion for Multi-Physics Emulation](https://mlsanity.com/paper/2410.13794/) (2024)
- [FNOPE: Simulation-based inference on function spaces with Fourier Neural Operators](https://mlsanity.com/paper/2505.22573/) (2025)
- [Efficient Autoregressive Inference for Transformer Probabilistic Models](https://mlsanity.com/paper/2510.09477/) (2025)
- [One Operator for Many Densities: Amortized Approximation of Conditioning by Neural Operators](https://mlsanity.com/paper/2605.06873/) (2026)
- [Amortized Bayesian Workflow](https://mlsanity.com/paper/2409.04332/) (2024)

## Abstract (arXiv)

Amortized Bayesian inference trains neural networks to solve stochastic inference problems using model simulations, thereby making it possible to rapidly perform Bayesian inference for any newly observed data. However, current simulation-based amortized inference methods are simulation-hungry and inflexible: They require the specification of a fixed parametric prior, simulator, and inference tasks ahead of time. Here, we present a new amortized inference method -- the Simformer -- which overcomes these limitations. By training a probabilistic diffusion model with transformer architectures, the Simformer outperforms current state-of-the-art amortized inference approaches on benchmark tasks and is substantially more flexible: It can be applied to models with function-valued parameters, it can handle inference scenarios with missing or unstructured data, and it can sample arbitrary conditionals of the joint distribution of parameters and data, including both posterior and likelihood. We showcase the performance and flexibility of the Simformer on simulators from ecology, epidemiology, and neuroscience, and demonstrate that it opens up new possibilities and application domains for amortized Bayesian inference on simulation-based models.