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.

翻译：形变是视觉与计算机图形学中长期存在的问题，需要依赖时间变化的扭曲以实现特征对齐，并通过混合实现平滑插值。近年来，多层感知机（MLPs）因其无网格性和可微性，被探索作为隐式神经表示（INRs）来建模此类变形；然而，从标准MLPs中提取连贯且准确的形变通常依赖于昂贵的正则化，这往往导致训练不稳定并阻碍有效的特征对齐。为克服这些限制，我们提出了FLOWING（FLOW morphING）框架，该框架将扭曲重新构建为微分向量流的构造，通过将结构流属性直接编码到网络架构中，自然确保了连续性、可逆性和时间一致性。这种以流为中心的方法产生了原理性且稳定的变换，实现了对二维图像和三维形状的精确且结构保持的形变。在包括人脸与图像形变以及高斯溅射形变在内的多种应用中进行的大量实验表明，FLOWING以更快的收敛速度实现了最先进的形变质量。代码与预训练模型可在 http://schardong.github.io/flowing 获取。