Research map / Probabilistic and scientific modeling / Variational and generative sampling
Normalizing Flows on Tori and Spheres
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the recursive Möbius-spline flow instead of the exponential-map polynomial flow | S² flows · S², four-mode mixture | KL [nats]: 0.50\,(0.09) -> 0.05\,(0.01) | Helped |
| Replace the polynomial scalar field with the radial scalar field | Exponential-map flow · S², four-mode mixture | KL [nats]: 0.82\,(0.30) -> 0.10\,(0.10) | Helped |
| Increase the number of stacked transformations from N_T=1 to N_T=6 and use K=5 radial components (ablation) | EMSRE · S², four-mode mixture | KL [nats]: 0.82\,(0.30) -> 0.19\,(0.05) | Helped |
| Use N_T=24 transformations with one radial component instead of N_T=1 with K=12 (ablation) | EMSRE · S², four-mode mixture | KL [nats]: 0.82\,(0.30) -> 0.10\,(0.10) | Helped |
| Use N_T=24 transformations with one radial component instead of N_T=6 with K=5 (ablation) | EMSRE · S², four-mode mixture | KL [nats]: 0.19\,(0.05) -> 0.10\,(0.10) | Helped |
| Use the recursive flow instead of an exponential-map flow | Sphere flows · S², four-mode mixture | ESS: 90\% vs 42\% (EMSRE, N_T=1, K=12); 90\% vs 85\% (EMSRE, N_T=24, K=1) | Helped |
| Use circular splines rather than Möbius or NCP flows for highly concentrated targets | Circle flows · T² targets | ESS | Hurt |
| Compose the spherical recursive flow with a learnable rotation (ablation) | Möbius-spline flow on S² · Non-axis-aligned density on S² | performance | No clear effect |
Closest papers by meaning
- Riemannian Continuous Normalizing Flows (NeurIPS 2020 · similarity 0.88)
- Analytic Bijections for Smooth and Interpretable Normalizing Flows (ICML 2026 · similarity 0.84)
- Implicit Normalizing Flows (ICLR 2021 · similarity 0.84)
- Flow Matching on General Geometries (ICLR 2024 · similarity 0.84)
- On the Universality of Volume-Preserving and Coupling-Based Normalizing Flows (ICML 2024 · similarity 0.83)
- Rectifying Categorical Flows on Statistical Manifolds for One-Step Generation (NeurIPS 2026 · similarity 0.83)
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