mlsanityData to 13 Oct 2026

i-flow: High-dimensional Integration and Sampling with Normalizing Flows

arXiv 2001.05486 ↗First posted 15 Jan 2020physics.comp-ph cs.LG hep-phcited by 26

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Abstract (arXiv)

In many fields of science, high-dimensional integration is required. Numerical methods have been developed to evaluate these complex integrals. We introduce the code i-flow, a python package that performs high-dimensional numerical integration utilizing normalizing flows. Normalizing flows are machine-learned, bijective mappings between two distributions. i-flow can also be used to sample random points according to complicated distributions in high dimensions. We compare i-flow to other algorithms for high-dimensional numerical integration and show that i-flow outperforms them for high dimensional correlated integrals. The i-flow code is publicly available on gitlab at https://gitlab.com/i-flow/i-flow.

Key facts. Cited by 26 papers in the map (data through 13 Oct 2026). First posted on arXiv 15 Jan 2020.

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2021: 9; 2022: 1; 2023: 5; 2024: 7; 2025: 1; 2026: 3.

26 papers.

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  1. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 178
  2. 2021Annealed Flow Transport Monte Carlocited by 90
  3. 2023Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimizationcited by 57
  4. 2021Machine Learning in the Search for New Fundamental Physicscited by 50
  5. 2024Improved off-policy training of diffusion samplerscited by 47
  6. 2021CaloFlow: Fast and Accurate Generation of Calorimeter Showers with Normalizing Flowscited by 46
  7. 2021Generative Networks for Precision Enthusiastscited by 21
  8. 2021Understanding Event-Generation Networks via Uncertaintiescited by 17
  9. 2022CaloFlow for CaloChallenge Dataset 1cited by 14
  10. 2024Convolutional L2LFlows: Generating Accurate Showers in Highly Granular Calorimeters Using Convolutional Normalizing Flowscited by 13
  11. 2021Latent Space Refinement for Deep Generative Modelscited by 10
  12. 2021Optimising simulations for diphoton production at hadron colliders using amplitude neural networkscited by 9
14 more
  1. 2023Calorimeter shower superresolutioncited by 7
  2. 2024Unifying Simulation and Inference with Normalizing Flowscited by 6
  3. 2026Scaling laws for amplitude surrogatescited by 6
  4. 2023Comparison of Affine and Rational Quadratic Spline Coupling and Autoregressive Flows through Robust Statistical Testscited by 5
  5. 2023Rare Event Probability Learning by Normalizing Flowscited by 3
  6. 2024BUFF: Boosted Decision Tree based Ultra-Fast Flow matchingcited by 3
  7. 2023Variational autoencoder with weighted samples for high-dimensional non-parametric adaptive importance samplingcited by 2
  8. 2024Extrapolating Jet Radiation with Autoregressive Transformerscited by 2
  9. 2026Generative Models and Statistical Validationcited by 2
  10. 2021Comparing Machine Learning and Interpolation Methods for Loop-Level Calculationscited by 1
  11. 2025BitHEP -- The Limits of Low-Precision ML in HEPcited by 1
  12. 2026CaloTrilogy: Toward a Breakthrough in One-Step, End-to-End, Physics-Guided Shower Generation for Modern Calorimeterscited by 1
  13. 2024An AI-powered Technology Stack for Solving Many-Electron Field Theorycited by 0
  14. 2024Flow Annealed Importance Sampling Bootstrap meets Differentiable Particle Physicscited by 0