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.
Dynamic 3D Gaussian Splatting methods achieve strong training-view PSNR on monocular video but generalize poorly: on the D-NeRF benchmark we measure an average train-test PSNR gap of 6.18 dB, rising to 11 dB on individual scenes. We report two findings that together account for most of that gap. Finding 1 (the role of splitting). A systematic ablation of the Adaptive Density Control pipeline (split, clone, prune, frequency, threshold, schedule) shows that splitting is responsible for over 80% of the gap: disabling split collapses the cloud from 44K to 3K Gaussians and the gap from 6.18 dB to 1.15 dB. Across all threshold-varying ablations, gap is log-linear in count (r = 0.995, bootstrap 95% CI [0.99, 1.00]), which suggests a capacity-based explanation. Finding 2 (the role of deformation coherence). We show that the capacity explanation is incomplete. A local-smoothness penalty on the per-Gaussian deformation field -- Elastic Energy Regularization (EER) -- reduces the gap by 40.8% while growing the cloud by 85%. Measuring per-Gaussian strain directly on trained checkpoints, EER reduces mean strain by 99.72% (median 99.80%) across all 8 scenes; on 8/8 scenes the median Gaussian under EER is less strained than the 1st-percentile (best-behaved) Gaussian under baseline. Alongside EER, we evaluate two further regularizers: GAD, a loss-rate-aware densification threshold, and PTDrop, a jitter-weighted Gaussian dropout. GAD+EER reduces the gap by 48%; adding PTDrop and a soft growth cap reaches 57%. We confirm that coherence generalizes to (a) a different deformation architecture (Deformable-3DGS, +40.6% gap reduction at re-tuned lambda), and (b) real monocular video (4 HyperNeRF scenes, reducing the mean PSNR gap by 14.9% at the same lambda as D-NeRF, with near-zero quality cost). The overfitting in dynamic 3DGS is driven by incoherent deformation, not parameter count.
3D Gaussian Splatting (3DGS) enables real-time novel view synthesis for static scenes. Extending it to dynamic scenes via deformation fields has recently attracted significant attention, particularly for dynamic scene reconstructionband distractor-free. However, existing deformation networks lack explicit motion awareness: they neither capture long-term motion intensity nor exploit short-term temporal coherence, leading to inaccurate foreground deformation and pseudo-static residuals in the background. We present MVFusion-GS, a method that enhances deformation networks with two complementary motion-aware mechanisms. The Motion-Variance Guided Refinement aggregates per-Gaussian deformation statistics across time to estimate motion variance and uses it to guide dynamic-static separation during deformation prediction. The MotionFormer Temporal Attention module applies Transformer self-attention over neighboring timesteps to model local motion dependencies and improve temporal consistency. Extensive experiments on both dynamic scene reconstruction and distractor-free reconstruction benchmarks demonstrate state-of-the-art performance, showing that explicit motion awareness improves both foreground motion modeling and static background reconstruction.
Three-dimensional Gaussian Splatting (3DGS) combines explicit primitives with efficient rasterization, yet recent systems increasingly use neural networks to generate or share Gaussian parameters. We characterize this trend along five axes: attribute decoding, spatial sharing, view-conditioned decoding, topology generation, and amortized inference. An analysis of 19 representative methods shows that these choices address different limitations and cannot be reduced to a binary neural label. We also isolate three forms of neural parameterization in a controlled mip-NeRF 360 study. Sharing appearance and opacity improves reconstruction quality, while decoding geometric structure offers no further gain. The evidence favors selective neuralization: shared functions help when they capture reusable correlations without sacrificing the local geometric freedom of explicit splats.