# PSRFlow: Probabilistic Super Resolution with Flow-Based Models for Scientific Data

arXiv: https://arxiv.org/abs/2308.04605 · HTML: https://mlsanity.com/paper/2308.04605/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 44 references that are in the map.
- First posted on arXiv 8 Aug 2023.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [Hierarchical Conditional Flow: A Unified Framework for Image Super-Resolution and Image Rescaling](https://mlsanity.com/paper/2108.05301/) (2021)
- [Volumetric Isosurface Rendering with Deep Learning-Based Super-Resolution](https://mlsanity.com/paper/1906.06520/) (2019)
- [Go with the Flows: Mixtures of Normalizing Flows for Point Cloud Generation and Reconstruction](https://mlsanity.com/paper/2106.03135/) (2021)
- [Deep Hierarchical Super Resolution for Scientific Data](https://mlsanity.com/paper/2107.00462/) (2021)
- [Uncertainty Visualization of 2D Morse Complex Ensembles Using Statistical Summary Maps](https://mlsanity.com/paper/1912.06341/) (2019)
- [Direct Volume Rendering with Nonparametric Models of Uncertainty](https://mlsanity.com/paper/2008.13576/) (2020)
- [Using VAEs and Normalizing Flows for One-shot Text-To-Speech Synthesis of Expressive Speech](https://mlsanity.com/paper/1911.12760/) (2019)
- [Exploratory Lagrangian-Based Particle Tracing Using Deep Learning](https://mlsanity.com/paper/2110.08338/) (2021)
- [Fiber Uncertainty Visualization for Bivariate Data With Parametric and Nonparametric Noise Models](https://mlsanity.com/paper/2207.11318/) (2022)
- [Visualizing Confidence Intervals for Critical Point Probabilities in 2D Scalar Field Ensembles](https://mlsanity.com/paper/2207.13661/) (2022)

## Built on by (most cited first, 8 of 8)

- [Boosting Flow-based Generative Super-Resolution Models via Learned Prior](https://mlsanity.com/paper/2403.10988/) (2024)
- [MRI Super-Resolution with Deep Learning: A Comprehensive Survey](https://mlsanity.com/paper/2511.16854/) (2025)
- [SurroFlow: A Flow-Based Surrogate Model for Parameter Space Exploration and Uncertainty Quantification](https://mlsanity.com/paper/2407.12884/) (2024)
- [CD-TVD: Contrastive Diffusion for 3D Super-Resolution with Scarce High-Resolution Time-Varying Data](https://mlsanity.com/paper/2508.08173/) (2025)
- [ConfEviSurrogate: A Conformalized Evidential Surrogate Model for Uncertainty Quantification](https://mlsanity.com/paper/2504.02919/) (2025)
- [Topology Guidance: Controlling the Outputs of Generative Models via Vector Field Topology](https://mlsanity.com/paper/2505.06804/) (2025)
- [REV-INR: Regularized Evidential Implicit Neural Representation for Uncertainty-Aware Volume Visualization](https://mlsanity.com/paper/2601.17689/) (2026)
- [Supervising the Path to Fine Scales: GalerkinFlow for Scientific-Field and Image Super-Resolution](https://mlsanity.com/paper/2608.16546/) (2026)

## Abstract (arXiv)

Although many deep-learning-based super-resolution approaches have been proposed in recent years, because no ground truth is available in the inference stage, few can quantify the errors and uncertainties of the super-resolved results. For scientific visualization applications, however, conveying uncertainties of the results to scientists is crucial to avoid generating misleading or incorrect information. In this paper, we propose PSRFlow, a novel normalizing flow-based generative model for scientific data super-resolution that incorporates uncertainty quantification into the super-resolution process. PSRFlow learns the conditional distribution of the high-resolution data based on the low-resolution counterpart. By sampling from a Gaussian latent space that captures the missing information in the high-resolution data, one can generate different plausible super-resolution outputs. The efficient sampling in the Gaussian latent space allows our model to perform uncertainty quantification for the super-resolved results. During model training, we augment the training data with samples across various scales to make the model adaptable to data of different scales, achieving flexible super-resolution for a given input. Our results demonstrate superior performance and robust uncertainty quantification compared with existing methods such as interpolation and GAN-based super-resolution networks.