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Neural Eulerian Scene Flow Fields
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Reframes scene flow as fitting a continuous space-time ODE with a neural prior, optimized test-time per sequence with multi-frame Chamfer and cycle-consistency losses, yielding EulerFlow.
Problem
Scene flow estimation from point clouds typically uses only two frames and struggles with small, fast-moving objects; existing methods do not exploit full observation sequences.
Approach
Model scene flow as an Eulerian ODE over position and time represented by a neural prior (extending NSFP's coordinate MLP with a time and direction input), optimized jointly over the full sequence with multi-step Euler-integrated Chamfer reconstruction and cycle-consistency losses; no canonical frame is needed and 3D point tracking emerges from solving the ODE.
Key results
- On the Argoverse 2 2024 Scene Flow Challenge, EulerFlow surpasses all prior art, beating the next-best unsupervised method (ICP Flow) by more than 2.5x in mean Dynamic Normalized EPE.
- EulerFlow exceeds the next-best supervised method (Flow4D) by over 10%.
- On Waymo Open, EulerFlow more than halves the error of the next best method.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use EulerFlow instead of ICP Flow | Argoverse 2 2024 Scene Flow Challenge · Argoverse 2 2024 Scene Flow Challenge test set | mean Dynamic Normalized EPE: >2.5× mean dynamic error reduction | Helped |
| Use EulerFlow instead of Flow4D | Argoverse 2 2024 Scene Flow Challenge · Argoverse 2 2024 Scene Flow Challenge test set | mean Dynamic Normalized EPE: over 10% | Helped |
| Use EulerFlow instead of the next-best method | Waymo Open scene flow · Waymo Open validation set | mean Dynamic Normalized EPE: more than halving the error | Helped |
| Increase observation sequence length (ablation) | EulerFlow · Argoverse 2 val split | mean Dynamic Normalized EPE | Helped |
| Use EulerFlow instead of NTP at sequence length 20 | Argoverse 2 val split · Argoverse 2 val split, sequence length 20 | mean Dynamic Normalized EPE | Helped |
| Remove multi-step Euler-integrated rollouts (No k>1) (ablation) | EulerFlow · Argoverse 2 val split | mean Dynamic Normalized EPE | Hurt |
| Remove cycle-consistency rollouts (No Cycle) (ablation) | EulerFlow · Argoverse 2 val split | mean Dynamic Normalized EPE | Mixed |
| Increase neural-prior depth from 8 to 18 (ablation) | EulerFlow · Argoverse 2 val split | mean Dynamic Normalized EPE: 0.1% worse | Helped |
| Increase neural-prior depth beyond 18 (ablation) | EulerFlow · Argoverse 2 val split | mean Dynamic Normalized EPE | Hurt |
| Replace normalized time with higher-frequency sinusoidal time embeddings (ablation) | EulerFlow · Argoverse 2 val split | mean Dynamic Normalized EPE | Hurt |
| Replace ReLU with SinC nonlinearity (ablation) | EulerFlow · Argoverse 2 val split | mean Dynamic Normalized EPE | Hurt |
| Replace ReLU with Gaussian nonlinearity (ablation) | EulerFlow · Argoverse 2 val split | mean Dynamic Normalized EPE | Hurt |
Surprising findings
- On two frames, EulerFlow collapses to NSFP, so its gains come from the multi-frame sequence optimization.
- Gaussian activations failed to converge and SinC and high-frequency time embeddings degraded performance, supporting the smooth ReLU prior.
Limitations
- Point cloud only; sparse lidar limits tracking of small objects, and RGB is not used.
- Expensive per-sequence optimization (about 24 hours per sequence on one V100).
- Chamfer distance does not model ray-casting geometry, causing false flow on moving shadows of occluders.
Experimental setup
Datasets: Argoverse 2 Waymo Open
Benchmarks: Argoverse 2 2024 Scene Flow Challenge Waymo Open Scene Flow
Metrics: mean Dynamic Normalized EPE per-class Dynamic Normalized EPE
Baselines: NSFP Fast NSF ZeroFlow FastFlow3D NTP Flow4D ICP Flow DeFlow SeFlow TrackFlow
Builds on: Neural Scene Flow Prior Neural Trajectory Prior Chamfer distance
Closest papers by meaning
- Flow-NeRF: Joint Learning of Geometry, Poses, and Dense Flow within Unified Neural Representations (CVPR 2025 · similarity 0.87)
- DeltaFlow: An Efficient Multi-frame Scene Flow Estimation Method (NeurIPS 2025 · similarity 0.86)
- MESSENGER: Memory-Enhanced Sequential Scene Flow Estimation via Autoregressive Next-Frame Forecasting (NeurIPS 2026 · similarity 0.85)
- ZeroFlow: Scalable Scene Flow via Distillation (ICLR 2024 · similarity 0.85)
- E-MoFlow: Learning Egomotion and Optical Flow from Event Data via Implicit Regularization (NeurIPS 2025 · similarity 0.84)
- Efficient Meshflow and Optical Flow Estimation from Event Cameras (CVPR 2024 · similarity 0.84)
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