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

Researchers propose replacing the MLP-based deformation field in Deformable 3D Gaussian Splatting with Liquid Neural Networks (LNNs), enabling truly continuous-time modeling of dynamic 3D scenes. The approach achieves performance parity or better than baseline methods while providing mathematically principled temporal smoothness, particularly excelling on scenes with complex articulated motion.

This research addresses a fundamental architectural mismatch in current dynamic 3D scene reconstruction methods. While Deformable 3D Gaussian Splatting (D-3DGS) uses positional-encoded MLPs that ostensibly operate on continuous time inputs, they effectively function as discrete per-frame predictors, requiring temporal smoothness to emerge indirectly through optimization pressure. The proposed solution substitutes Closed-form Continuous-time (CfC) cells from Liquid Neural Networks, which mathematically encode temporal dynamics through sigmoidal time gates that interpolate between learned hidden states. This approach embeds smooth temporal behavior directly into the loss landscape rather than relying on numerical solvers, reducing computational overhead while improving explicit continuity properties.

The technical contribution represents a practical advancement in neural rendering pipelines that reconstruct dynamic content from monocular video. By preserving all other D-3DGS components and demonstrating performance gains on 15 established benchmark scenes, the work validates LNNs as a drop-in replacement rather than requiring architectural redesign. Performance improvements concentrate on high-frequency articulated motion scenarios, suggesting the method particularly benefits dynamic scenes with complex deformations—commercially relevant for animation, visual effects, and motion capture applications.

The broader significance lies in demonstrating how principled continuous-time modeling outperforms implicit approaches in specialized domains. For the computer vision and neural rendering communities, this validates LNNs as viable alternatives to standard architectures for temporal modeling tasks. The zero-friction integration pathway encourages adoption in existing pipelines, potentially accelerating deployment in production rendering systems where temporal quality and computational efficiency directly impact pipeline costs and output fidelity.

• →Liquid Neural Networks provide mathematically continuous temporal modeling for 3D scene deformation without numerical solvers
• →Performance matches or exceeds MLP baselines across benchmarks with largest gains on articulated motion scenes
• →Architecture functions as drop-in replacement, enabling adoption in existing D-3DGS pipelines without redesign
• →Sigmoidal time gates embed smooth temporal response directly into optimization landscape rather than relying on emergent properties
• →Approach validates continuous-time methods over discrete per-frame prediction for dynamic scene reconstruction