FLOWING: Implicit Neural Flows for Structure-Preserving Morphing

TL;DR

FLOWING addresses the challenge of coherent structure preserving morphing by reframing warping as learning a continuous time dependent flow using flow based implicit neural representations. It leverages Neural ODEs and Neural Conjugate Flows to model the warp while enforcing continuity invertibility and temporal coherence by construction, supplemented by a thin plate like regularizer and a forward differentiation acceleration. The approach yields near instant training and strong alignment for 2D images and 3D Gaussian splatting, enabling effective blending with generative models for high fidelity morphs. Across face, image, and 3D morphing tasks, FLOWING achieves state of the art quality with fast convergence and robust structure preservation, demonstrating practical impact for interactive editing, view synthesis, and 3D morphing pipelines.

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.

Figures (11)

• Figure 1: We present FLOWING, a robust and theoretically grounded framework for fast, accurate, and structure-preserving morphing. It enables smooth and temporally consistent morphs by learning a structure-preserving flow, applicable to both 2D (top-left) and 3D (top-right) data; the latter uses 3DGS for representing 3D faces. Bottom-left: FLOWING instantly aligns landmarks by construction, outperforming SoTA methods in both visual quality and convergence speed. Bottom-right: Integrating FLOWING with generative models improves morphing fidelity and semantic coherence.
• Figure 2: Overview of FLOWING. Given source and target images $I^0 , I^1$ we extract landmark pairs $(p^0_i,p^1_i)$ with a feature extractor (dlib, Xfeat, etc). We train a flow $\phi$ such that $\phi(p^0,t) = \phi(p^1,t-1)$, effectively mapping $p^0$ to $p^1$. At inference, we warp $I^0$ forward by $t$ units and $I^1$ and backward by $t-1$ units, then blend them together with methods such as linear blending or generative models.
• Figure 3: Comparison between ifmorph and FLOWING. While ifmorph fails to preserve structure, FLOWING produces clean and realistic interpolations by enforcing flow properties such as invertibility and trajectory uniqueness.
• Figure 4: Convergence analysis of ifmorph (green), NCF (orange), and NODE (violet). Left: alignment and deformation metrics over training steps. For NODE, alignment is measured using the Jacobian term, while ifmorph and NCF use the Hessian-based thin-plate term. Right: qualitative morphing results at $t=0.5$ after $100$, $1000$, $2000$, $10000$, and $20000$ training steps. NCF and NODE achieve accurate alignment by $1000$ steps, whereas ifmorph requires at least $2000$ steps.
• Figure 5: Applications of FLOWING to view interpolation (Rows 1-3), and stylization and object morphing (Rows 4-6). FLOWING produces smooth transitions even under environmental variations, maintaining geometric and photometric consistency. When combined with DiffMorpher, it further enhances structural coherence and visual fidelity, recovering details missed by DiffMorpher alone, such as the missing chimneys and the loss of column detail (Rows 2-3).