Important Points
1. Higher Degrees of Freedom (4D) Gaussian Primitives

FreeTimeGS takes a different path from some other recent works. Rather than training a heavy, global deformation field, the authors give each Gaussian primitive with its own simple linear motion function. By only modeling short-range shifts between primitives and the observed scene, this approach sidesteps the ill-posedness of fitting a full warp and keeps optimization both stable and less expensive. Each primitive still learns its spatial position, orientation, scale, velocity, temporal center, duration, opacity, and spherical-harmonic coefficients.
2. 4D Regularization
Optimizing FreeTimeGS with only rendering losses can result in reaching local minima in fast-moving regions, where some primitives become fully opaque which blocks gradient flow to others. To address this, the authors add a regularization term that penalizes high spatial opacity early in training while detaching the temporal opacity from gradients. This helps ensure all primitives remain semi-transparent initially, promoting better gradient propagation which subsequently leads to higher-quality reconstructions in dynamic regions.
3. Periodic Relocation
While 4D regularization improves rendering quality, it often increases the number of primitives required. To maintain a more compact representation, FreeTimeGS implements a periodic relocation strategy where after every fixed number of iterations, low-opacity primitives are moved to areas with high photometric or opacity gradients. This targeted resampling concentrates primitives where they are most needed for more efficient coverage.
Critique
I would have liked a comparison with the Shape of Motion paper since FreeTimeGS and Shape of Motion are quite similar in assigning linear transformations to individual Gaussians.
Concluding Thoughts
Despite mentions of relying on per-scene optimization and not supporting relighting, I think this work is promising just from the merit of significantly outperforming other SOTA models.