# Bifidelity Parameter Estimation Using Conditional Diffusion Models

arXiv: https://arxiv.org/abs/2504.01894 · HTML: https://mlsanity.com/paper/2504.01894/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 35 of its 62 references that are in the map.
- First posted on arXiv 2 Apr 2025.

## Placed in

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

## Builds on (most cited first, 30 of 35)

- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery](https://mlsanity.com/paper/1703.05921/) (2017)
- [Adversarial Uncertainty Quantification in Physics-Informed Neural Networks](https://mlsanity.com/paper/1811.04026/) (2018)
- [FlowSeq: Non-Autoregressive Conditional Sequence Generation with Generative Flow](https://mlsanity.com/paper/1909.02480/) (2019)
- [Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation](https://mlsanity.com/paper/2006.00702/) (2020)
- [Provable Probabilistic Imaging using Score-Based Generative Priors](https://mlsanity.com/paper/2310.10835/) (2023)
- [Conditional Sampling with Monotone GANs: from Generative Models to Likelihood-Free Inference](https://mlsanity.com/paper/2006.06755/) (2020)
- [Neural Methods for Amortized Inference](https://mlsanity.com/paper/2404.12484/) (2024)
- [An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems](https://mlsanity.com/paper/2309.00983/) (2023)
- [Learning Stochastic Dynamical System via Flow Map Operator](https://mlsanity.com/paper/2305.03874/) (2023)
- [Data-Driven Model Reduction for the Bayesian Solution of Inverse Problems](https://mlsanity.com/paper/1403.4290/) (2014)
- [Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference](https://mlsanity.com/paper/2310.16975/) (2023)
- [A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems](https://mlsanity.com/paper/2410.03108/) (2024)
- [Score-based generative models are provably robust: an uncertainty quantification perspective](https://mlsanity.com/paper/2405.15754/) (2024)
- [Conditional Injective Flows for Bayesian Imaging](https://mlsanity.com/paper/2204.07664/) (2022)
- [Diffusion-Model-Assisted Supervised Learning of Generative Models for Density Estimation](https://mlsanity.com/paper/2310.14458/) (2023)
- [Modeling Unknown Stochastic Dynamical System via Autoencoder](https://mlsanity.com/paper/2312.10001/) (2023)
- [A transport-based multifidelity preconditioner for Markov chain Monte Carlo](https://mlsanity.com/paper/1808.09379/) (2018)
- [Bi-fidelity Variational Auto-encoder for Uncertainty Quantification](https://mlsanity.com/paper/2305.16530/) (2023)
- [A Score-based Nonlinear Filter for Data Assimilation](https://mlsanity.com/paper/2306.09282/) (2023)
- [Taming Score-Based Diffusion Priors for Infinite-Dimensional Nonlinear Inverse Problems](https://mlsanity.com/paper/2405.15676/) (2024)
- [Context-aware surrogate modeling for balancing approximation and sampling costs in multi-fidelity importance sampling and Bayesian inverse problems](https://mlsanity.com/paper/2010.11708/) (2020)

## Built on by (most cited first, 7 of 7)

- [Effortless, Simulation-Efficient Bayesian Inference using Tabular Foundation Models](https://mlsanity.com/paper/2504.17660/) (2025)
- [Diffusion Models in Simulation-Based Inference: A Tutorial Review](https://mlsanity.com/paper/2512.20685/) (2025)
- [Multilevel neural simulation-based inference](https://mlsanity.com/paper/2506.06087/) (2025)
- [Training-free score-based diffusion for parameter-dependent stochastic dynamical systems](https://mlsanity.com/paper/2602.02113/) (2026)
- [Instance-Wise Adaptive Sampling for Dataset Construction in Approximating Inverse Problem Solutions](https://mlsanity.com/paper/2509.04583/) (2025)
- [Conservative neural posterior estimation via distributionally robust training](https://mlsanity.com/paper/2605.28516/) (2026)
- [AECSF: Adaptive Ensemble Conditional Score Filtering for High-Dimensional Nonlinear Data Assimilation](https://mlsanity.com/paper/2609.32411/) (2026)

## Abstract (arXiv)

We present a bifidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional parameter estimation methods rely on repeated simulations of potentially expensive forward models to determine the posterior distribution of the parameter values, which may result in computationally intractable workflows. Furthermore, methods such as Markov Chain Monte Carlo (MCMC) necessitate rerunning the entire algorithm for each new data observation, further increasing the computational burden. Hence, we propose a novel method for efficiently obtaining posterior distributions of parameter estimates for high-fidelity models given data observations of interest. The method first constructs a low-fidelity, conditional generative model capable of amortized Bayesian inference and hence rapid posterior density approximation over a wide-range of data observations. When higher accuracy is needed for a specific data observation, the method employs adaptive refinement of the density approximation. It uses outputs from the low-fidelity generative model to refine the parameter sampling space, ensuring efficient use of the computationally expensive high-fidelity solver. Subsequently, a high-fidelity, unconditional generative model is trained to achieve greater accuracy in the target posterior distribution. Both low- and high- fidelity generative models enable efficient sampling from the target posterior and do not require repeated simulation of the high-fidelity forward model. We demonstrate the effectiveness of the proposed method on several numerical examples, including cases with multi-modal densities, as well as an application in plasma physics for a runaway electron simulation model.