GaussianFlesh: A Unified Gaussian Substrate for Physics-Grounded 4D World Models
GaussianFlesh is a simulation substrate in which 3D Gaussian particles are both the rendered primitive and the material point used by continuum mechanics. Each particle stores kinematic state, rest and deformed covariance, deformation gradient, material parameters, thermodynamic state, and phase. During simulation, all particles scatter to a shared Updated Lagrangian MLS-MPM grid, but each particle dispatches to its own constitutive law during P2G: corotated elasticity for rubber-like materials, StVK with log-strain J2 return mapping for metal plasticity, Drucker-Prager return mapping for clay/sand, and a compressible bulk-modulus pressure law for molten fluid.
Physically grounded scene representations usually split appearance from dynamics. Neural or Gaussian scene representations store geometry and radiance, while a separate simulator advances proxy particles, meshes, cages, or grids. This separation makes it hard to assign material identity locally, to preserve the appearance of captured objects during deformation, and to express phase changes or plasticity without converting between representations.
GaussianFlesh treats every Gaussian as a material point. Material identity is the primary key, instantiated before reconstruction, not inferred from it. A consequence is that appearance and material behavior are decoupled at the identity level: opacity and color are invariant to material assignment, while covariance push-forward makes physical deformation visible in splat shape.
Per-particle constitutive dispatch
The core mechanism is a shared UL-MLS-MPM grid with per-particle constitutive dispatch during P2G. During the transfer from particle to grid, each particle reads its own material model ID and evaluates the appropriate stress law. All particles couple through the same grid. Multi-material coupling therefore occurs through the mass-weighted grid velocity field rather than through explicit pairwise constraints.
The dispatch is per particle, not per object. A single connected Gaussian object can have a metal region, a rubber region, and a molten region sharing one grid. The system supports corotated elasticity for rubber and jelly, StVK/log-strain J2 plasticity for metal (with work hardening and permanent deformation), Drucker-Prager return mapping for clay and sand, and compressible fluid pressure for molten material.
Thermomechanics
Heat diffuses on the same grid once per display frame. Before the melt point, shear modulus weakens continuously as temperature rises. At the melt point, excess heat fills a latent-heat buffer while temperature holds steady. Once the buffer saturates, the particle switches to fluid phase. This supports bottom-up melt fronts and solid/fluid coexistence within the same particle cloud, with the boundary determined by local temperature history.
Trained 3DGS assets
GaussianFlesh can load trained 3D Gaussian Splatting PLY point clouds directly and paint material identity per particle. The learned covariance, opacity, and spherical-harmonic appearance are preserved. A photoreal ficus or pillow can be simulated as rubber, metal, jelly, or a per-particle mixture without changing its visual texture — because appearance and physics are decoupled at the identity level.
Why it matters for world models
World models currently lack a grounded physics primitive. Video-based approaches learn correlations from pixels and cannot represent that a rubber ball and a metal ball behave differently for reasons that can be computed. A substrate where any object can be instantiated, assigned a material identity, and simulated forward in the same Gaussian space used for scene reconstruction closes that loop.
Future work will introduce vision-driven automatic material inference, closing the loop between scene understanding and physical instantiation entirely.