mlsanityData to 14 Oct 2026

TO-FLOW: Efficient Continuous Normalizing Flows with Temporal Optimization adjoint with Moving Speed

arXiv 2203.10335 ↗First posted 19 Mar 2022cs.CVcited by 8

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Abstract (arXiv)

Continuous normalizing flows (CNFs) construct invertible mappings between an arbitrary complex distribution and an isotropic Gaussian distribution using Neural Ordinary Differential Equations (neural ODEs). It has not been tractable on large datasets due to the incremental complexity of the neural ODE training. Optimal Transport theory has been applied to regularize the dynamics of the ODE to speed up training in recent works. In this paper, a temporal optimization is proposed by optimizing the evolutionary time for forward propagation of the neural ODE training. In this appoach, we optimize the network weights of the CNF alternately with evolutionary time by coordinate descent. Further with temporal regularization, stability of the evolution is ensured. This approach can be used in conjunction with the original regularization approach. We have experimentally demonstrated that the proposed approach can significantly accelerate training without sacrifying performance over baseline models.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 57 of its 78 references that are in the map. First posted on arXiv 19 Mar 2022.

Builds on

57 of 78 references.

References · 57

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  3. 2017Proximal Policy Optimization Algorithmscited by 15,215
  4. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
  5. 2018Neural Ordinary Differential Equationscited by 3,779
  6. 2015Variational Inference with Normalizing Flowscited by 2,170
  7. 2016Density estimation using Real NVPcited by 2,042
  8. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,545
  9. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
  10. 2014NICE: Non-linear Independent Components Estimationcited by 1,058
  11. 2017Masked Autoregressive Flow for Density Estimationcited by 684
  12. 2016Improving Variational Inference with Inverse Autoregressive Flowcited by 640
38 more
  1. 2019Neural Spline Flowscited by 596
  2. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 594
  3. 2019Augmented Neural ODEscited by 397
  4. 2018WaveGlow: A Flow-based Generative Network for Speech Synthesiscited by 309
  5. 2019Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Designcited by 262
  6. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 250
  7. 2020How to train your neural ODE: the world of Jacobian and kinetic regularizationcited by 228
  8. 2018Neural Autoregressive Flowscited by 208
  9. 2019BSP-Net: Generating Compact Meshes via Binary Space Partitioningcited by 206
  10. 2018Neural Importance Samplingcited by 155
  11. 2019NASA: Neural Articulated Shape Approximationcited by 149
  12. 2020Riemannian Continuous Normalizing Flowscited by 145
  13. 2020OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transportcited by 143
  14. 2020Normalizing Flows on Tori and Spherescited by 117
  15. 2019GraphNVP: An Invertible Flow Model for Generating Molecular Graphscited by 116
  16. 2019Noise Flow: Noise Modeling with Conditional Normalizing Flowscited by 108
  17. 2019Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noisecited by 101
  18. 2019Unconstrained Monotonic Neural Networkscited by 92
  19. 2019ANODE: Unconditionally Accurate Memory-Efficient Gradients for Neural ODEscited by 84
  20. 2019On Robustness of Neural Ordinary Differential Equationscited by 83
  21. 2020Learning Differential Equations that are Easy to Solvecited by 81
  22. 2017Maximum Principle Based Algorithms for Deep Learningcited by 78
  23. 2020Adaptive Checkpoint Adjoint Method for Gradient Estimation in Neural ODEcited by 76
  24. 2019Latent Normalizing Flows for Discrete Sequencescited by 67
  25. 2020Targeted free energy estimation via learned mappingscited by 67
  26. 2020STEER: Simple Temporal Regularization For Neural ODEscited by 58
  27. 2018FloWaveNet : A Generative Flow for Raw Audiocited by 54
  28. 2019Leveraging exploration in off-policy algorithms via normalizing flowscited by 46
  29. 2021MALI: A memory efficient and reverse accurate integrator for Neural ODEscited by 42
  30. 2020Vid-ODE: Continuous-Time Video Generation with Neural Ordinary Differential Equationcited by 40
  31. 2019Improving Exploration in Soft-Actor-Critic with Normalizing Flows Policiescited by 38
  32. 2018Layer-Parallel Training of Deep Residual Neural Networkscited by 35
  33. 2019Deep learning as optimal control problems: models and numerical methodscited by 34
  34. 2020Model-based Reinforcement Learning for Semi-Markov Decision Processes with Neural ODEscited by 32
  35. 2019SNODE: Spectral Discretization of Neural ODEs for System Identificationcited by 26
  36. 2021Multi-scale Neural ODEs for 3D Medical Image Registrationcited by 18
  37. 2019Universal audio synthesizer control with normalizing flowscited by 17
  38. 2018Randomized Value Functions via Multiplicative Normalizing Flowscited by 15

50 most cited of 57 All 57 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 0; 2024: 2; 2025: 3; 2026: 2.

8 papers.

  1. 2022Flow Matching for Generative Modelingcited by 5,702
  2. 2025X-IL: Exploring the Design Space of Imitation Learning Policiescited by 10
  3. 2024Entropy-Informed Weighting Channel Normalizing Flow for Deep Generative Modelscited by 5
  4. 2026A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimationcited by 3
  5. 2024Sparse Variational Student-t Processes for Heavy-tailed Modelingcited by 2
  6. 2025Efficient Manifold-Constrained Neural ODE for High-Dimensional Datasetscited by 2
  7. 2026Flow matching on homogeneous spacescited by 1
  8. 2025Instance Relation Learning Network with Label Knowledge Propagation for Few-shot Multi-label Intent Detectioncited by 0