Research map / Probabilistic and scientific modeling / Variational and generative sampling
Ergodic Generative Flows
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes Ergodic Generative Flows (EGFs), built from finitely many globally defined diffeomorphisms whose generated group is ergodic, with a tractable flow-matching loss and a KL-weakFM loss for imitation learning without a separate reward model.
Problem
Training generative flow networks in continuous spaces is hampered by intractable flow-matching losses, the need for a separate reward model in imitation learning, difficulty handling cycles/ergodic 0-flows, and expressivity limits with few transformations.
Approach
Construct the forward policy from finitely many diffeomorphisms (e.g., affine maps on tori, rotations on spheres) whose generated group is topologically ergodic, giving a closed-form backward policy and star inflow so the FM loss is tractable; universality follows from ergodicity and spectral-gap (summable L2-mixing) arguments, and a KL-weakFM loss combines cross-entropy with a weak flow-matching
Key results
- On the NASA volcano dataset, EGFN reaches NLL -2.31 versus -2.02 for Moser Flow and -0.31 for mixture vMF.
- On earthquake and flood datasets EGFN also gets the best NLL (-0.12 and 0.56), outperforming Moser Flow (-0.09 and 0.62).
- On the toy 2D IL task, a minimal EGF with four affine torus transformations reproduces the target while Moser Flow with the same small 32x3 model fails to train.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use EGFN instead of Moser Flow | spherical NASA datasets · Volcano | negative log-likelihood: -2.02 -> -2.31 | Helped |
| use EGFN instead of Moser Flow | spherical NASA datasets · Earthquake | negative log-likelihood: -0.09 -> -0.12 | Helped |
| use EGFN instead of Moser Flow | spherical NASA datasets · Flood | negative log-likelihood: 0.62 -> 0.56 | Helped |
| add regularization R to the unstable FM loss (ablation) | EGF RL training · 2D checkerboard RL task | training stability | Helped |
| replace the divergence-based FM loss with stable FM loss (ablation) | EGF RL training · 2D checkerboard RL task | training stability | Helped |
| increase the depth of the alpha policy network rather than the outflow network (ablation) | EGF · 2D toy tasks | generated distribution quality | Helped |
| increase network depth and width beyond depth 4 (ablation) | EGF · 2D toy tasks | training stability | Hurt |
| filter low-density stopping points during inference (ablation) | EGF · Volcano | negative log-likelihood | Helped |
| use a minimal EGF instead of a small Moser Flow | imitation learning models · 2D toy distributions on the torus | distribution reproduction quality | Helped |
Surprising findings
- The unstable divergence-based FM loss blows up in the checkerboard RL task while the stable loss converges, supporting the predicted instability from ergodic 0-flows.
- The EGF reportedly uses a model about 30 times smaller than the baseline while outperforming it on volcano data.
Limitations
- Experiments are restricted to low-dimensional settings (2D tori and spheres).
- Universality relies on L2-mixing summability, which is hard to enforce or verify in higher dimensions.
- Hyperparameter tuning was minimal and the density filter threshold is selected on validation data.
Experimental setup
Datasets: NASA volcano dataset NASA earthquake dataset NASA flood dataset toy 2D distributions (checkerboard, spin wheel, 4 circles, 2 spirals)
Benchmarks: NASA volcano dataset NASA earthquake dataset NASA flood dataset toy 2D checkerboard RL task
Metrics: negative log-likelihood flow-matching loss stability sampling time
Baselines: Moser Flow Mixture vMF Stereographic Riemannian Detailed balance Trajectory balance
Builds on: generative flow networks Moser Flow detailed balance trajectory balance normalizing flows
Closest papers by meaning
- Flow Factorization for Efficient Generative Flow Networks (AAAI 2025 · similarity 0.90)
- Beyond Squared Error: Exploring Loss Design for Enhanced Training of Generative Flow Networks (ICLR 2025 · similarity 0.88)
- A Theory of Non-acyclic Generative Flow Networks (AAAI 2024 · similarity 0.88)
- Pre-Training and Fine-Tuning Generative Flow Networks (ICLR 2024 · similarity 0.88)
- Looking Backward: Retrospective Backward Synthesis for Goal-Conditioned GFlowNets (ICLR 2025 · similarity 0.87)
- Revisiting Non-Acyclic GFlowNets in Discrete Environments (ICML 2025 · similarity 0.87)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.