FOLIAGE: Towards Physical Intelligence World Models Via Unbounded Surface Evolution

Physical intelligence -- anticipating and shaping the world from partial, multisensory observations -- is critical for next-generation world models. We propose FOLIAGE, a physics-informed multimodal world model for unbounded accretive surface growth. In its Action-Perception loop, a unified context encoder maps images, mesh connectivity, and point clouds to a shared latent state. A physics-aware predictor, conditioned on physical control actions, advances this latent state in time to align with the target latent of the surface, yielding a Modality-Agnostic Growth Embedding (MAGE) that interfaces with critic heads for downstream objectives. FOLIAGE's Accretive Graph Network (AGN) captures dynamic connectivity through Age Positional Encoding and Energy-Gated Message-Passing. Geometry-Correspondence Fusion and Cross-Patch Masking enhance MAGE's expressiveness, while Hierarchical Pooling balances global context with local dynamics. We create SURF-GARDEN, a world model learning platform comprising a Counterfactual Physics Simulator, a Multimodal Correspondence Extractor, and Evolution Tracing, which generates 7,200 diverse surface-growth sequences. SURF-BENCH, our physical-intelligence evaluation suite, evaluates six core tasks -- topology recognition, inverse material estimation, growth-stage classification, latent roll-out, cross-modal retrieval, and dense correspondence -- and four stress tests -- sensor dropout, zero-shot modality transfer, long-horizon prediction, and physics ablation -- to probe resilience. FOLIAGE outperforms specialized baselines while remaining robust across dynamic environments, establishing a new world-model based, multimodal pathway to physical intelligence.

@article{liu2025_2506.03173,
  title={ FOLIAGE: Towards Physical Intelligence World Models Via Unbounded Surface Evolution },
  author={ Xiaoyi Liu and Hao Tang },
  journal={arXiv preprint arXiv:2506.03173},
  year={ 2025 }
}