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arxiv: 2606.29976 · v1 · pith:5KKFRO7Inew · submitted 2026-06-29 · 💻 cs.CV

Learning Efficient 4D Gaussian Representations from Monocular Videos with Flow Splatting

Shengjun Zhang , Jinzhao Li , Xin Fei , Yueqi Duan This is my paper

Pith reviewed 2026-06-30 06:55 UTC · model grok-4.3

classification 💻 cs.CV
keywords 4D Gaussian splattingdynamic scene reconstructionmonocular videosoptical flowvelocity fieldnovel view synthesisflow splatting
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The pith

Flow Splatting renders optical flow from 4D Gaussian velocity fields to supervise efficient dynamic scene reconstruction from monocular videos.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes Flow Splatting to learn 4D Gaussian representations from monocular videos by constructing a velocity field from time-varying means and covariances. This field is then splatted using an extended volume rendering approach that accounts for camera motion, producing optical flow to supervise the dynamics without ground-truth data. The approach addresses long training times, low rendering speeds, and high memory use in prior 4D extensions of Gaussian splatting. A sympathetic reader would care because the method claims to deliver higher image quality with reduced training time and increased rendering speed on standard benchmarks.

Core claim

We extend 4D volumes with time varying means and covariance to represent complex dynamics. Then, we construct and approximate the velocity field naturally based on this representations. While conventional volume rendering techniques support to render color fields, we extend the volume rendering strategy to splat the velocity field by considering the influence of camera motions. This enables Flow Splatting to render optical flow from the velocity field to supervise the dynamics learning process from monocular videos.

What carries the argument

Flow Splatting: the extension of conventional splatting to render optical flow by approximating and splatting the velocity field constructed from time-varying 4D Gaussian means and covariances while accounting for camera motion.

If this is right

  • The model achieves better image quality than state-of-the-art methods.
  • Training requires less time consumption than prior 4D Gaussian extensions.
  • Rendering speed is higher while maintaining or improving quality.
  • The representation avoids high memory consumption associated with per-frame 4D volumes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The velocity-field approximation might be adapted to supply other dense signals such as depth or surface normals in monocular settings.
  • The same splatting extension could be applied to non-Gaussian representations that already output time-varying positions.
  • If the camera-motion correction holds across wide baselines, the method could support reconstruction from casually captured handheld videos without additional calibration.

Load-bearing premise

The velocity field naturally constructed from time-varying 4D Gaussian means and covariances can be accurately approximated and splatted to provide reliable optical-flow supervision without introducing artifacts or requiring ground-truth flow.

What would settle it

A direct comparison on a controlled dynamic sequence where the rendered optical flow from the approximated velocity field deviates substantially from ground-truth motion or produces worse reconstruction metrics than baselines would falsify the reliability of the supervision signal.

Figures

Figures reproduced from arXiv: 2606.29976 by Jinzhao Li, Shengjun Zhang, Xin Fei, Yueqi Duan.

Figure 1
Figure 1. Figure 1: Comparison of previous methods and ours. (a) We visualize the rendering results of color and optical flow for our baseline [63] and Flow Splatting. (b) We report PSNR and the rendering speed on the NVIDIA dataset [66] for multiple methods. The size of circle represents training time. Gaussians is not maintained as in physical world with insufficient viewpoints [16], leading to visual overfitting, performan… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of our framework. We first leverage off-the-shelf models to predict optical flow, depth maps, masks and trajectories for the input monocular video. Then, we initialize the foreground and background respectively from the data-driven priors. Apart from the color field, we construct velocity field and propose the flow splatting strategy to render optical flow from velocity field. We introduce both co… view at source ↗
Figure 3
Figure 3. Figure 3: Qualitative Comparison on the Davis dataset. We present the qualitative comparison between our method and previous methods for novel view and novel time synthesis. 4.2 Main Results Quantitative and Qualitative Results. We conduct experiments for novel view synthesis on the NVIDIA dataset [66] and report the quantitative results in [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Qualitative Comparison of optical flow. We render the optical flow of all methods with flow splatting. The baseline stands for 4DGS [63] which presents the 4D volume. w/o 4D Gaussian indicates the absence of Polynomials and Fourier series. w/o velocity loss represents that the method is trained without supervision on the velocity field. w/o initialization means that the initialization is replaced by random… view at source ↗
read the original abstract

Reconstructing dynamic 3D scenes from monocular videos is challenging due to scene complexity and temporal dynamics. With the advancement of 3D Gaussian Splatting in novel view synthesis, existing methods extend 3D Gaussians to 4D domain with deformation fields, trajectories or spatiotemporal 4D volumes to model scene element deformation. However, these methods suffer from long training time, low rendering speed or high memory consumption for per-frame reconstruction of 4D volumes, without fully exploiting dense dynamic information. To address this issue, we propose Flow Splatting, which constructs the velocity field and enables the conventional splatting technique to render optical flow from the velocity field to supervise dynamics learning process from monocular videos. Specifically, we extend 4D volumes with time varying means and covariance to represent complex dynamics. Then, we construct and approximate the velocity field naturally based on this representations. While conventional volume rendering techniques support to render color fields, we extend the volume rendering strategy to splat the velocity field by considering the influence of camera motions. We conduct experiments on various benchmarks to demonstrate the efficiency and effectiveness of our method. Compared to the state-of-the-art methods, our model achieves better image quality with less time consumption and higher rendering speed.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes Flow Splatting, an extension of 4D Gaussian Splatting for dynamic scene reconstruction from monocular videos. It represents scenes with time-varying 4D Gaussians (means and covariances), constructs and approximates a velocity field from these, and extends volume rendering to splat the velocity field (accounting for camera motion) to render optical flow as a supervision signal for learning dynamics. Experiments on benchmarks claim superior image quality, reduced training time, and higher rendering speed versus prior SOTA methods that use deformation fields, trajectories, or full 4D volumes.

Significance. If the velocity-field approximation and camera-aware splatting prove reliable, the method could provide an efficient, monocular-only supervision mechanism that avoids external flow networks or per-frame 4D volumes, improving training speed and rendering performance for dynamic novel-view synthesis.

major comments (2)
  1. [Method description of velocity-field construction and approximation] The central claim that the approximated velocity field yields reliable optical-flow supervision (and thereby the reported quality/time gains) lacks any derivation, error bound, or quantitative validation of approximation accuracy. This construction is load-bearing for the supervision signal yet is described only qualitatively in the abstract and method overview.
  2. [Experiments and ablation studies] No ablation or analysis is reported on how the velocity-field splatting behaves under non-rigid motion or fast camera movement—the exact regimes where the skeptic concern predicts artifacts that would bias dynamics learning. Such controls are required to substantiate that the supervision signal remains artifact-free.
minor comments (2)
  1. The abstract and method summary contain no equations for the velocity-field approximation or the extended splatting integral; adding these would clarify the technical contribution.
  2. Quantitative comparisons would benefit from explicit reporting of training time, rendering FPS, and memory usage alongside PSNR/SSIM/LPIPS on the same hardware and scenes as the cited SOTA baselines.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the two major comments point by point below, indicating the revisions we will incorporate.

read point-by-point responses

  1. Referee: [Method description of velocity-field construction and approximation] The central claim that the approximated velocity field yields reliable optical-flow supervision (and thereby the reported quality/time gains) lacks any derivation, error bound, or quantitative validation of approximation accuracy. This construction is load-bearing for the supervision signal yet is described only qualitatively in the abstract and method overview.

    Authors: We agree that the manuscript would benefit from a more formal treatment. The velocity field is obtained by taking the time derivative of the time-varying Gaussian means (and, for the covariance term, the appropriate Lie-algebra derivative), which directly yields an instantaneous velocity at each Gaussian center; this field is then splatted with the same alpha-blending weights used for color. In the revision we will add an explicit derivation subsection together with a first-order error bound that follows from the local linearity assumption of the Gaussian motion model. We will also report a quantitative validation: on synthetic sequences with known ground-truth flow we measure the L2 discrepancy between the splatted flow and the analytic flow, confirming that the approximation error remains below 0.5 pixels on average under the motion regimes present in our benchmarks. revision: yes

  2. Referee: [Experiments and ablation studies] No ablation or analysis is reported on how the velocity-field splatting behaves under non-rigid motion or fast camera movement—the exact regimes where the skeptic concern predicts artifacts that would bias dynamics learning. Such controls are required to substantiate that the supervision signal remains artifact-free.

    Authors: The main experiments already include scenes with pronounced non-rigid deformation and moderate-to-fast camera motion (e.g., the D-NeRF and HyperNeRF sequences). Nevertheless, we concur that isolating these factors would strengthen the claims. In the revised manuscript we will add two controlled ablations: (1) synthetic non-rigid sequences with increasing deformation magnitude, reporting PSNR, flow error, and training time; (2) real sequences with artificially accelerated camera trajectories, measuring the same metrics. These results will be presented in a new subsection of the experiments. revision: yes

Circularity Check

0 steps flagged

No load-bearing circularity; supervision signal treated as external to fitted parameters.

full rationale

The paper extends 4D Gaussian volumes with time-varying means/covariances, constructs an approximated velocity field from them, and extends splatting to render optical flow for supervising dynamics. This construction does not reduce any claimed prediction or result to a fitted input by definition, nor does it rely on a self-citation chain for uniqueness or ansatz. The central efficiency/quality claims rest on the method's ability to use the rendered flow as supervision from monocular video, which the text presents as an independent signal rather than a tautological renaming or self-fit. Minor self-citations (standard for Gaussian splatting extensions) are not load-bearing for the derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; the method implicitly relies on standard volume-rendering assumptions and the claim that velocity can be derived directly from time-varying Gaussian parameters.

axioms (1)
  • domain assumption Conventional volume rendering can be extended to splat velocity fields while accounting for camera motion.
    Stated directly in the abstract as the basis for rendering optical flow.

pith-pipeline@v0.9.1-grok · 5756 in / 1144 out tokens · 32052 ms · 2026-06-30T06:55:55.250149+00:00 · methodology

discussion (0)

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Reference graph

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