# FOLIAGE: Towards Physical Intelligence World Models Via Unbounded Surface Evolution

arXiv: https://arxiv.org/abs/2506.03173 · HTML: https://mlsanity.com/paper/2506.03173/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 45 of its 72 references that are in the map.
- First posted on arXiv 29 May 2025.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Builds on (most cited first, 30 of 45)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Is Space-Time Attention All You Need for Video Understanding?](https://mlsanity.com/paper/2102.05095/) (2021)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [VideoMAE V2: Scaling Video Masked Autoencoders with Dual Masking](https://mlsanity.com/paper/2303.16727/) (2023)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Habitat 2.0: Training Home Assistants to Rearrange their Habitat](https://mlsanity.com/paper/2106.14405/) (2021)
- [PointCLIP: Point Cloud Understanding by CLIP](https://mlsanity.com/paper/2112.02413/) (2021)
- [PointNeXt: Revisiting PointNet++ with Improved Training and Scaling Strategies](https://mlsanity.com/paper/2206.04670/) (2022)
- [VideoMamba: State Space Model for Efficient Video Understanding](https://mlsanity.com/paper/2403.06977/) (2024)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [ULIP-2: Towards Scalable Multimodal Pre-training for 3D Understanding](https://mlsanity.com/paper/2305.08275/) (2023)
- [CrossPoint: Self-Supervised Cross-Modal Contrastive Learning for 3D Point Cloud Understanding](https://mlsanity.com/paper/2203.00680/) (2022)
- [Sim-to-Real via Sim-to-Sim: Data-efficient Robotic Grasping via Randomized-to-Canonical Adaptation Networks](https://mlsanity.com/paper/1812.07252/) (2018)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [CLIP2Point: Transfer CLIP to Point Cloud Classification with Image-Depth Pre-training](https://mlsanity.com/paper/2210.01055/) (2022)

## Built on by (most cited first, 2 of 2)

- [A Comprehensive Survey on World Models for Embodied AI](https://mlsanity.com/paper/2510.16732/) (2025)
- [World Models for Embodied Intelligence: From Plausible to Controllable to Actionable](https://mlsanity.com/paper/2609.16697/) (2026)

## Abstract (arXiv)

Many physical systems do not merely move or deform; they grow, adding material and changing the geometry that a world model must represent. Existing world models are typically optimized for pixel prediction, reward prediction, or fixed-support physical dynamics, leaving open how to model systems whose underlying physical support expands over time and whose future morphology depends on hidden material response. We introduce FOLIAGE, a geometry-centered latent world model for growing surfaces. Within a fixed state budget, FOLIAGE represents mature regions as a compact scaffold while allocating higher-resolution state to regions predicted to drive near-future growth. This focuses representation and computation where new material and geometric change occur while retaining compact global context. FOLIAGE further separates observation, action, and privileged physics: heterogeneous RGB, point-cloud, and mesh observations are fused into a deployable geometric state; material controls condition the latent dynamics; and hidden physical energies guide training but are not required at deployment. To evaluate this setting, we introduce SURF-GARDEN and SURF-BENCH, providing controlled counterfactual branches, dense cross-modal correspondences, hidden physical signals, and stress tests for growing-geometry state learning. FOLIAGE reduces inverse-material error by ≈40% and 5-step mesh forecasting Chamfer error by ≈30% relative to strong baselines, while improving cross-modal retrieval by +14 mAP points. Stress tests show graceful degradation under sensor loss and correspondence corruption. On temporal 3D plant scans, FOLIAGE also improves passive future-geometry forecasting, while transfer experiments show that the learned geometry-centered state remains useful beyond the simulator.