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FLOWING: Implicit Neural Flows for Structure-Preserving Morphing
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Proposes FLOWING, a flow-based implicit neural representation (NODE and NCF with SIREN activations and thin-plate regularization) for structure-preserving 2D image, face, and 3D Gaussian splatting morphing from sparse landmarks.
Problem
Morphing requires a time-dependent warp that aligns features and stays invertible and coherent; generic MLP-based INRs need costly regularization, train unstably, and can produce singularities and artifacts.
Approach
Recast warping as a differential vector flow built into the architecture (neural ODEs or neural conjugate flows with sinusoidal activations), so continuity, invertibility, and temporal coherence hold by construction, with only a thin-plate Jacobian penalty and a forward-mode differentiation scheme for speed.
Key results
- NCF (SIREN) and NODE (SIREN) reduce landmark alignment MSE by one to three orders of magnitude relative to ifmorph on FRLL, MegaDepth and NeRSemble (e.g., FRLL 3.9E-5 and 1.4E-4 vs 1.5E-3).
- On FRLL linear blending, NODE achieves LPIPS 0.210/0.213 and FID 31.952, beating ifmorph (0.250/0.252, FID 38.427) and OpenCV in LPIPS.
- A forward-mode differentiation scheme makes the thin-plate loss computation 23.4x faster than autograd (6.93e-3 s vs 1.62e-1 s per iteration).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SIREN rather than sigmoid activations (ablation) | FLOWING NCF and NODE · FRLL landmark alignment | landmark alignment MSE: NCF: 8.7E-3 -> 3.9E-5; NODE: 6.2E-2 -> 1.4E-4 | Helped |
| Use SIREN rather than sigmoid activations (ablation) | FLOWING NCF and NODE · MegaDepth landmark alignment | landmark alignment MSE: NCF: 2.0E+1 -> 4.2E-4; NODE: 1.9E-1 -> 4.9E-4 | Helped |
| Use SIREN rather than sigmoid activations (ablation) | FLOWING NCF and NODE · NeRSemble landmark alignment | landmark alignment MSE: NCF: 7.2E-5 -> 7.3E-5; NODE: 5.0E-4 -> 5.9E-5 | Mixed |
| Add thin-plate regularization (ablation) | NODE · MegaDepth trajectory approximation | maximum squared error: 5.44E-05 -> 6.43E-07 (3 steps); 3.39E-08 -> 3.27E-09 (5 steps); 1.88E-09 -> 5.24E-10 (7 steps); 8.88E-12 -> 5.18E-10 (15 | Helped |
| Add thin-plate regularization (ablation) | NODE · FRLL trajectory approximation | maximum squared error: 1.36E-07 -> 7.16E-10 (3 steps); 2.08E-10 -> 6.19E-11 (5 steps); 5.46E-11 -> 6.00E-11 (7 steps); 5.46E-11 -> 6.10E-11 (15 | Mixed |
| Vary NODE integration steps (ablation) | FLOWING NODE · MegaDepth and FRLL trajectory approximation | maximum squared error | Mixed |
| Use forward differentiation instead of autograd for Hessian computation (ablation) | FLOWING NCF thin-plate loss · 1,000 domain points | iteration time: 1.62 × 10^{-1} seconds -> 6.93 × 10^{-3} seconds; 23.4× speed-up | Helped |
| Add thin-plate regularization (ablation) | ifmorph · Morphing deformation smoothness and structural coherence | visual deformation quality | Helped |
| Add thin-plate regularization (ablation) | FLOWING NCF and NODE · Morphing deformation smoothness and structural coherence | visual deformation quality | Helped |
| Use FLOWING warping before DiffMorpher blending | DiffMorpher · Image morphing | structural coherence and visual fidelity | Helped |
| Use union-based 3D Gaussian blending rather than blending rendered images | FLOWING 3DGS morphing · 3D face morphing | transition coherence and ghosting | Helped |
| Use NODE rather than NCF | FLOWING · FRLL linear face morphing | FID: 33.300 -> 31.952 | Helped |
Surprising findings
- NODE converges quickly and with 2k steps trains in about 16 seconds, but it shows poorer feature alignment than NCF in landmark MSE.
- On FRLL linear blending, OpenCV Delaunay morphing achieves better FID (32.426) than NCF (33.300).
Limitations
- Invertibility by construction means it cannot model occlusions or topology changes such as open versus closed mouths.
- Depends on accuracy of landmark correspondences from manual or automatic detectors.
- NODE morphing is slower at high resolution (1.48 s at 1350^2) than ifmorph and OpenCV.
Experimental setup
Datasets: FRLL MegaDepth NeRSemble FFHQ Sintel
Benchmarks: FRLL MegaDepth NeRSemble Sintel
Metrics: MSE LPIPS FID training time morphing time
Baselines: ifmorph OpenCV Delaunay morphing DiffMorpher thin-plate spline warping Optical Flow Warp Linear Blend
Builds on: ifmorph SIREN neural ODE neural conjugate flows DiffMorpher 3D Gaussian splatting
Closest papers by meaning
- Wukong's 72 Transformations: High-fidelity Textured 3D Morphing via Flow Models (NeurIPS 2025 · similarity 0.88)
- Neural Implicit Morphing of Face Images (CVPR 2024 · similarity 0.86)
- Flow-Corrected Shape Optimization: Taming Manifold Drift in High-Dimensional 3D Models (NeurIPS 2026 · similarity 0.86)
- Flow-NeRF: Joint Learning of Geometry, Poses, and Dense Flow within Unified Neural Representations (CVPR 2025 · similarity 0.86)
- IMPUS: Image Morphing with Perceptually-Uniform Sampling Using Diffusion Models (ICLR 2024 · similarity 0.86)
- FlowDrag: 3D-aware Drag-based Image Editing with Mesh-guided Deformation Vector Flow Fields (ICML 2025 · similarity 0.85)
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