Liquid Neural Networks as a Drop-in Continuous-Time Deformation Field for Dynamic 3D Gaussian Splatting

• URL: http://arxiv.org/abs/2606.07670v1
• Date: Thu, 04 Jun 2026 08:43:44 GMT
• Title: Liquid Neural Networks as a Drop-in Continuous-Time Deformation Field for Dynamic 3D Gaussian Splatting
• Abstract summary: Deformable 3D Gaussian Splatting (D-3DGS) re-constructs dynamic scenes from monocular video by deforming a canonical set of 3Ds through a positional-encoded Gaussian of frame time t.<n>We optimisation the deformation field as a stack of Closed-form Continuous-time cells, a Liquid Neural Network (LNN)<n>The result is a near-zero-friction architectural design that turns the discrete deformation field into an explicit continuous-time function of t.
• Score: 4.1711003960475495
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Deformable 3D Gaussian Splatting (D-3DGS) re-constructs dynamic scenes from monocular video by deforming a canonical set of 3D Gaussians through a positional-encoded MLP of frame time t. Although fitted to a continuous variable, the MLP couples no two values of t in its architecture and effectively predicts discrete per-frame offsets, leaving temporal smoothness to emerge only as a byproduct of optimisation. We redesign the deformation field as a stack of Closed-form Continuous-time (CfC) cells, a Liquid Neural Network (LNN), that is the closed-form solution of the Liquid Time-constant ODE while preserving every other part of the D-3DGS pipeline. Each cell exposes a sigmoidal time gate that interpolates between two candidate hidden states, baking a learned smooth response to t into the loss landscape without invoking any numerical solver. On the eight D-NeRF and seven NeRF-DS scenes the liquid field matches or exceeds the MLP baseline in aggregate, with its largest gains concentrated on the scenes with the most high-frequency articulated motion. The result is a near-zero-friction architectural design that turns the discrete MLP deformation field into an explicit continuous-time function of t.

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