Research map / Probabilistic and scientific modeling / Variational and generative sampling
Riemannian Continuous Normalizing Flows
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Riemannian CNF instead of naive Euclidean CNF | CNFs on the Poincaré disk · Wrapped Gaussian targets on the Poincaré disk | maximum-likelihood fit | Helped |
| Use Riemannian CNF instead of wrapped CNF | CNFs on the Poincaré disk · Wrapped Gaussian targets on the Poincaré disk | maximum-likelihood fit | Helped |
| Use Riemannian CNF instead of stereographic CNF | CNFs on the sphere · vMF target at the stereographic projection point | negative log-likelihood | Helped |
| Use Riemannian CNF instead of stereographic CNF | CNFs on the sphere · vMF target at the stereographic projection point | reverse KL | Helped |
| Use Riemannian CNF instead of stereographic CNF | CNFs on the sphere · vMF targets away from the projection point | fit quality | No clear effect |
| Use Riemannian CNF instead of stereographic CNF | Spherical density estimators · Volcano eruptions, earthquakes, floods, and wildfires | negative test log-likelihood | Helped |
| Use Riemannian CNF instead of a mixture of vMF distributions | Spherical density estimators · Volcano eruptions, earthquakes, floods, and wildfires | negative test log-likelihood | Helped |
| Use Riemannian CNF instead of stereographic CNF | Spherical density estimators · Volcano eruptions, earthquakes, floods, and wildfires | convergence speed | Helped |
| Add metric-aware rescaling to the vector-field output layer (ablation) | Riemannian CNF · Wrapped Gaussian targets on the Poincaré disk | number of function evaluations | Helped |
| Add metric-aware rescaling to the vector-field output layer (ablation) | Riemannian CNF · Wrapped Gaussian targets on the Poincaré disk | convergence speed | Helped |
| Add a geodesic distance input layer (ablation) | Riemannian CNF · Hyperbolic geometry | model performance | Helped |
| Add a geodesic distance input layer (ablation) | Riemannian CNF · Spherical geometry | model performance | No clear effect |
Closest papers by meaning
- Matching Normalizing Flows and Probability Paths on Manifolds (ICML 2022 · similarity 0.89)
- Normalizing Flows on Tori and Spheres (ICML 2020 · similarity 0.88)
- Flow Matching on General Geometries (ICLR 2024 · similarity 0.87)
- Injective flows for star-like manifolds (ICLR 2025 · similarity 0.86)
- Generative Modeling on Manifolds Through Mixture of Riemannian Diffusion Processes (ICML 2024 · similarity 0.84)
- Riemannian Consistency Model (NeurIPS 2025 · similarity 0.84)
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