We introduce PowerSim, a method to bring physically grounded, differentiable dynamics to PowerFoam’s power diagram based 3D representation. PowerSim directly couples a pre-trained PowerFoam scene to the Material Point Method (MPM) by exploiting a natural alignment between the two. As a result, simulated motion can drive the scene’s geometry and appearance directly, without an auxiliary representation in between. Built on this framework, we enable a range of applications on real and synthetic scenes: (1) simulating a static scene under user interaction, (2) recovering spatially varying material fields, (3) compositing primitives from independently captured scenes into a single simulation-ready scene and (4) ray-tracing reflections that update consistently as the object deforms. Our results suggest that PowerSim excels over previous frameworks for physically grounded dynamics, while unlocking unique advantages—such as secondary ray lighting effects on dynamic scenes.
PowerSim partitions the reconstructed object volume into explicit cells, while PhysGaussian uses Gaussian kernels that tend to concentrate near surfaces and optionally adds interior particles. Under extreme stretching with the same applied force, PAC-NeRF loses texture and develops abrupt cut-like boundaries, while PhysGaussian exhibits pronounced blurring in stretched regions. PowerSim retains more surface detail and sharper boundaries during separation.
After N MPM substeps, we leverage the deformation gradient output to update primitive positions, isotropically scale their radii to match local volume change, and rotate their dipole frames and appearance directions. We then rebuild adjacency for the updated primitives. Insets show two selected primitives before and after deformation.
Under the same applied force, random material assignment produces large stem bending, while PhysDreamer produces little bending. PowerSim produces back-and-forth motion with visible stem deformation. The first row shows the material field (Young’s modulus) for each setting.
Material Field (Young’s Modulus)
Simulation Results
We showcase a range of simulation results that demonstrate the versatility of PowerSim in reproducing different material behaviors, from collision and compression to elasticity and granular flow.
Collision
Compression
Elasticity
Granular
Mic Drop
Telephone Swinging
Single Physics Simulation in Garden Scene
Multi-Physics Simulation in Cafeteria Scene
We provide qualitative comparisons on the GSO drop benchmark with other baseline methods. Panels left to right: PAC-NeRF, PhysDreamer, Ours, Reference.
Mario
Bus
We model the bread as an elastic material and apply twisting and pulling to test the updates under large deformation. Under large twisting deformations, updating both the dipole frames and appearance directions helps preserve the object's geometry and appearance. We compare the full update with variants that hold either component fixed, and with PhysGaussian.
PowerSim
Fixed Dipole Plane
Fixed Detail Site Axis
PhysGaussian
PowerSim can select and move the telephone handset, but its motion exposes poorly reconstructed regions, revealing gaps and visual artifacts. This could be further improved by generative priors which help to complete these regions, which we leave to future work.
@misc{nguyen2026powersimdifferentiablephysicssimulation,
title={PowerSim: Differentiable Physics Simulation and Rendering with Power Diagrams},
author={Trong-Tung Nguyen and Anand Bhattad},
year={2026},
eprint={2609.38153},
archivePrefix={arXiv},
primaryClass={cs.CV},
url={https://arxiv.org/abs/2609.38153},
}We are grateful to Shrisudhan Govindarajan for his great discussion and helpful insights about PowerFoam, which our work is built upon.