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Stochastic Liquid Deformation Fields: An SDE Generalisation of Closed-Form Continuous-Time Cells for Dynamic 3D Gaussian Splatting

arXiv · AI, language, vision and robotics · article · Aug 27, 2026 · UTC

Deformable 3D Gaussian Splatting (D-3DGS) reconstructs dynamic scenes by deforming a canonical set of 3D Gaussians through a deformation field of frame time. Replacing its MLP with a stack of Closed-form Continuous-time (CfC) cells-a Liquid Neural Network that solves the Liquid Timeconstant ODE in closed form-gives the field continuous-time behaviour at feed-forward cost. That closed form, however, is only the deterministic limit of a noise-driven system, and drops the stochastic term usually credited for the robustness of liquid networks. We put it back: a small Gaussian perturbation is added

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