Advanced Topics · research-grade
World Models for Robotics: the math, the proofs, the tricks.
A world model is a robot's imagination: a learned model \(p(\text{future} \mid \text{past}, \text{actions})\) it can roll forward to plan, dream, and act. This module builds the idea from scratch and then walks the literature paper by paper, from Ha & Schmidhuber to RSSM/Dreamer, TD-MPC, JEPA / V-JEPA 2, diffusion world models, and 2026 frontier work, with the real math, step-through proofs you unfold yourself, an animation of how each model works, and a citation for every paper.
How to read this
Every model is dissected the same way.
- Intuition & why it matters for robots.
- The math: each equation with a plain-English reading and a symbol legend.
- Proof, step by step. Unfold the derivation one move at a time; each step has a "why this move?" with the assumption or trick it uses.
- Animation: watch the model's mechanism run.
- Assumptions · tricks · why this math · the fun part, then the citation.
The deck
Pick a model.
Grouped by era. Start with Foundations if the math is new.
How the ideas connect
One family tree.
Two big lineages, reconstruct-the-world (generative / latent dynamics) and predict-in-representation (JEPA), both flowing toward planning on real robots. Open any model to see what it builds on and what it leads to.
References
Every paper discussed.
Click a title to open it on arXiv. This module is a teaching companion to the primary sources, so read them.
Anchor survey: Hou et al., World Model for Robot Learning: A Comprehensive Survey (2026), arXiv:2605.00080.
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