FLOWING: Implicit Neural Flows for Structure-Preserving Morphing

2025-10-10

AI Summary

This work addresses the instability, feature misalignment, and structural distortion commonly observed in MLP-based deformation modeling due to heavy explicit regularization. To resolve these issues, we propose an implicit neural deformation framework grounded in differential vector fields. Methodologically, deformation is formulated as the solution of a continuous, invertible, and temporally consistent ordinary differential equation (ODE), with differential-geometric priors intrinsically embedded in the network architecture—eliminating the need for explicit regularization. By jointly optimizing an implicit neural representation and an MLP to solve the ODE-defined deformation trajectory, our approach enables end-to-end learning across diverse modalities, including 2D images, 3D faces, and Gaussian splatting. Experiments demonstrate state-of-the-art performance in deformation quality, structural correspondence accuracy, and temporal smoothness, alongside significantly accelerated convergence. The method achieves both computational efficiency and high geometric fidelity.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Morphing is a long-standing problem in vision and computer graphics, requiring a time-dependent warping for feature alignment and a blending for smooth interpolation. Recently, multilayer perceptrons (MLPs) have been explored as implicit neural representations (INRs) for modeling such deformations, due to their meshlessness and differentiability; however, extracting coherent and accurate morphings from standard MLPs typically relies on costly regularizations, which often lead to unstable training and prevent effective feature alignment. To overcome these limitations, we propose FLOWING (FLOW morphING), a framework that recasts warping as the construction of a differential vector flow, naturally ensuring continuity, invertibility, and temporal coherence by encoding structural flow properties directly into the network architectures. This flow-centric approach yields principled and stable transformations, enabling accurate and structure-preserving morphing of both 2D images and 3D shapes. Extensive experiments across a range of applications - including face and image morphing, as well as Gaussian Splatting morphing - show that FLOWING achieves state-of-the-art morphing quality with faster convergence. Code and pretrained models are available at http://schardong.github.io/flowing.

Problem

• Solving unstable training in neural morphing with flow-based architecture
• Ensuring structure preservation in 2D/3D morphing through differential flows
• Overcoming costly regularization needs for coherent feature alignment

Innovation

• Uses differential vector flow for warping
• Encodes flow properties into network architecture
• Enables structure-preserving morphing for 2D/3D