Title: FLOWING: Implicit Neural Flows for Structure-Preserving Morphing
Venue: NeurIPS 2025
Accepted: yes
Keywords: flows

implicit neural representations

morphing

warping
Abstract: Morphing is a long-standing problem in vision and computer graphics, requir-
ing 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 prop-
erties 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 in
https://schardong.github.io/flowing.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a flow-based implicit neural representation to estimate the vector flow to morph a source into a target one. By casting the problem as learning a time-dependent diffeomorphism, this method avoids expensive regularization overheads and naturally guarantees continuity, invertibility and temporal coherence. This method can generalize to both 2D and 3D inputs, exhibiting its huge generalization ability of the framework. The training target consists of two simple terms, a data penalty to ensure temporal coherence and invertibility, and a regularization term on flow Jacobian to ensure continuity and smoothness. At inference, the learned flow warps images or 3D Gaussian‐splat representations, followed by linear or generative blending for smooth interpolation. The authors adapt Neural ODE and Neural Conjugate Flows to solve their defined problem, and both achieves reasonable results.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n- The method applies flow-based implicit neural representation to estimate the flow for warping. Since the formulation satisfies an ODE, the method naturally overcomes the difficulty of temporal coherence and continuity.\n- Great versatility. This method can be solved by different architectures, and be applied to both 2D and 3D data, as well as both feature space and data (images or 3D points) space.\n### Weakness\n- No discussion on the computational efficiency.\n- The definition of $\\mathcal{F}^0$ at L162 seems wrong. For $i = 0$, the parameter should be $t$.\n- Likewise to Equation. 8\n\nQUESTIONS:\n- How much does this method rely on the accuracy of the correspondence pair?\n- Due to the implicit formulation, I wonder how efficient this method is compared to other methods?\n- In the 3D case, how many Gaussian blobs are used? What if the source Gaussians have a significantly different number of blobs from the target one?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

comments: SUMMARY:
Given an annotated set of corresponding points in a fixed and moving image, this paper trains a neural network to interpolate between these corresponding points.

STRENGTHS AND WEAKNESSES:
It's interesting to visually see the flow field from when the pre-existing NODE and NCF algorithms are applied to 2-D points, although NCF in particular is being used as something of a chainsaw cutting tissue paper- the work in NCF was needed for interpolating in extremely high dimensional spaces such as pixel intensities of RGB images.

The practicality of this approach seems dubious to me. It seems like an enormous amount of machinery and computation to replace a thin plate spline or delauney triangulation: the improvement over the opencv baseline in table 2 seems marginal. 

It would be more convincing if the authors had picked one of NCF or NODE- the two proposed approaches seem to have little in common to make this a single paper.

The improvement over the INR baseline is dramatic and real- if you already have a correspondence oracle but are absolutely determined that the correspondence between the remaining points in the image will be achieved by training an MLP, then this approach is correct.

QUESTIONS:
The main comparison that I'm interested in is the comparison to the OpenCV baseline in table 2. To convince me to increase my score, the main avenue would be to convince me that OpenCV's warping algorithm is seriously well tuned for VPIP, and so this method is impressive for edging it out- for example, if you show that you did some hyperparameter search for the OpenCV baseline on this task, or that this is a benchmark task that the OpenCV authors were aware of and were optimizing for.

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 3
IMPACT: 1
ORIGINALITY: 1
DATE: 2025-07-03

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes FLOWING, a framework for morphing between 2D images and 3D Gaussian splats using flow-based implicit neural representations. The method leverages Neural ODEs and Neural Conjugate Flows to ensure continuity, invertibility, and temporal coherence by construction, avoiding expensive regularizations used in prior work like ifmorph. The approach demonstrates applications in face morphing, image interpolation, and 3D Gaussian Splatting morphing.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**:\n- Quantitative results in Table 1 and Table 2 show striking improvements: for example, mean squared alignment errors drop by orders of magnitude on the FRLL and MegaDepth datasets when using the SIREN-activated NCF/NODE models compared to ifmorph. LPIPS and FID scores for image blending in Table 2 further highlight the superiority of FLOWING for perceptual quality.\n- FLOWING converges much faster and with more stability than ifmorph, which is susceptible to singularities and unstable warps.\n- Versatility for 2D and 3D\n- The method can be augmented by generative blending (e.g., DiffMorpher) after flow-based alignment, yielding visually superior morphs in diverse scenarios.\n\n**Weaknesses**\n- Flow-based morphing is widely applied in other domains, such as medical image registration (Voxelmporph-diff). Neural ODE-based solutions are also well-explored, such as NODEO (CVPR22), Neural Diffeomorphic Flow (CVPR22) and NMF (NeurIPS 2020). It is unclear what novel theoretical contributions are beyond prior works.\n- Though the landmark-based formulation is effective for faces or some designed datasets, the approach's reliance on accurate correspondences may limit applicability to scenarios where dense or reliable landmark annotations are unavailable or ambiguous, such as unconstrained scenes or many non-human objects.\n- The claim that minimizing Jacobian/Hessian norms produces plausible, semantically reasonable morphs is plausible but not universally justified, especially in settings where \"wiggly\" but valid transitions may be preferred in some tasks.\n- No Comparison with Learning-Free Flow Methods: Method comparisons seem limited to ifmorph and OpenCV warping. The inclusion of established, learning-free or classical flow-based approaches (e.g., dense optical flow with smoothing) would help contextualize FLOWING’s place among \"classic methods\" and modern INR-based approaches.\n\nQUESTIONS:\n- How does FLOWING perform on datasets lacking clearly defined landmark structures, such as natural scenes with heavy occlusion or clutter, or on domains outside conventional faces (e.g., animals, medical images)? Is it possible to relax landmark reliance?\n- Could you quantify and compare compute/memory requirements and wall-clock times for the main approaches (FLOWING vs. ifmorph vs. classical), especially as input/image sizes or landmark counts scale?\n- How does FLOWING compare to classical, non-learning-based flow warping (e.g., dense optical flow, thin-plate spline warping), both quantitatively and qualitatively on the main datasets?\n\nLIMITATIONS:\nYes; limitations are discussed—primarily in acknowledgment of ablation experiments and practical constraints—but further explicit analysis of error/failure cases and dataset diversity would strengthen the discussion.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-04"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes a structure preserving morphing mechanism which is based on Neural ODEs. The reason for using Neural ODE is because it naturally provides features like invertibility and temporarily smooth. This line of thinking has been used in several works such as in shape deformation so having a similar line o attack for the problem of morphing makes sense. The theoretical development presented in the paper is sound and rather straightforward. In addition to the flow based morphing approach, the paper leverages specialised implicit neural representations (INRs) to represent complex data such as images, etc. The paper includes several morphing experiments including extensions such as morphing of 3dGS and latent space morphing which open up exciting research directions.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: \n\n1. The simplicity of the framework, I argue is a major strength. NODEs are a very powerful class of models which come with several advantages such as invertibility by construction. Using them for the problem of morphing is an interesting idea. \n\n2. Instead of naively applying NODE to morphing, the paper uses vision encoders to first map images in feature space and then learn the flows between source and target images. I think this underlying idea can very well be generalisable to other problems in computer vision and seeing its promise for the problem of morphing is interesting. \n\n3. The paper shows both qualitatively and quantitatively superiority over prior art and includes interesting applications such as with 3DGS morphing and use of generative blending. \n\n\nWeakness. \n\n1. As with most NODE based approaches, I suspect there would be complications due to numerical errors in solving the initial value problem as well as slower speed. The paper hasn't sufficiently discussed these aspects.\n\nQUESTIONS:\n1. A section on limitations would be helpful. \n\n2. I am not clear why a vanilla NODE applied on the features (where t=0 is source and t=1 is target) won't work for morphing? Can the authors elucidate this point in more detail?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-05"}