# ProWorld: Progress-Aware Hyperbolic World Models for Long-Horizon Visual Goal Reaching

arXiv: https://arxiv.org/abs/2608.01926 · HTML: https://mlsanity.com/paper/2608.01926/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 26 of its 37 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Placed in

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

## Builds on (most cited first, 26 of 26)

- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Recurrent World Models Facilitate Policy Evolution](https://mlsanity.com/paper/1809.01999/) (2018)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [TD-MPC2: Scalable, Robust World Models for Continuous Control](https://mlsanity.com/paper/2310.16828/) (2023)
- [DINO-WM: World Models on Pre-trained Visual Features enable Zero-shot Planning](https://mlsanity.com/paper/2411.04983/) (2024)
- [Deep Visual Foresight for Planning Robot Motion](https://mlsanity.com/paper/1610.00696/) (2016)
- [Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images](https://mlsanity.com/paper/1506.07365/) (2015)
- [LeWorldModel: Stable End-to-End Joint-Embedding Predictive Architecture from Pixels](https://mlsanity.com/paper/2603.19312/) (2026)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristics](https://mlsanity.com/paper/2511.08544/) (2025)
- [OGBench: Benchmarking Offline Goal-Conditioned RL](https://mlsanity.com/paper/2410.20092/) (2024)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Search on the Replay Buffer: Bridging Planning and Reinforcement Learning](https://mlsanity.com/paper/1906.05253/) (2019)
- [Hyperbolic Vision Transformers: Combining Improvements in Metric Learning](https://mlsanity.com/paper/2203.10833/) (2022)
- [Hyperbolic Image Segmentation](https://mlsanity.com/paper/2203.05898/) (2022)
- [Objective Mismatch in Model-based Reinforcement Learning](https://mlsanity.com/paper/2002.04523/) (2020)
- [Long-Horizon Visual Planning with Goal-Conditioned Hierarchical Predictors](https://mlsanity.com/paper/2006.13205/) (2020)
- [Goal-Aware Prediction: Learning to Model What Matters](https://mlsanity.com/paper/2007.07170/) (2020)
- [Causal-JEPA: Learning World Models through Object-Level Latent Masking](https://mlsanity.com/paper/2602.11389/) (2026)
- [Sub-JEPA: Subspace Gaussian Regularization for Stable End-to-End World Models](https://mlsanity.com/paper/2605.09241/) (2026)
- [A Lightweight Library for Energy-Based Joint-Embedding Predictive Architectures](https://mlsanity.com/paper/2602.03604/) (2026)
- [HMamba: Hyperbolic Mamba for Sequential Recommendation](https://mlsanity.com/paper/2505.09205/) (2025)
- [Learning Along the Arrow of Time: Hyperbolic Geometry for Backward-Compatible Representation Learning](https://mlsanity.com/paper/2506.05826/) (2025)
- [Bending the Future: Autoregressive Modeling of Temporal Knowledge Graphs in Curvature-Variable Hyperbolic Spaces](https://mlsanity.com/paper/2209.05635/) (2022)

## Built on by (most cited first, 3 of 3)

- [Memory Has Geometry: Non-Uniform Geometric Memory for Long-Horizon Personalized AI](https://mlsanity.com/paper/2609.17969/) (2026)
- [Finite-Sample Metric Non-Collapse for Geometrically Supervised Latent World Models in Control](https://mlsanity.com/paper/2608.07265/) (2026)
- [Beyond a single latent space: a dual-latent world model for long-horizon planning](https://mlsanity.com/paper/2609.37644/) (2026)

## Abstract (arXiv)

JEPA-style visual world models offer an effective paradigm for visual goal planning by predicting future latent representations. Existing methods typically learn local transition consistency through next-step representation prediction. However, in long-horizon tasks, accurate local prediction alone need not ensure sustained progress toward the goal. First, multi-step rollouts can remain locally plausible while drifting away from goal-relevant trajectories. Second, locally similar future states can correspond to substantially different long-term progress, making them difficult to distinguish in a latent space optimized mainly for local consistency. To address these challenges, we introduce goal-conditioned progress order, a relative ordering of states according to how they advance toward a given goal. This order exhibits an asymmetric, coarse-to-fine structure: early states retain broader future possibilities, while later states concentrate on more specific goal-relevant regions. Such a structure is well suited to hyperbolic geometry. Motivated by this observation, we propose ProWorld, a progress-aware hyperbolic visual world model. ProWorld leverages goal-conditioned progress order to organize visual latent-space dynamics, maintains directional progress within trajectories via hyperbolic entailment learning, and mitigates progress ambiguity among locally similar future states via hyperbolic future discrimination. Furthermore, we design a progress-aware planning objective that scores candidate rollouts by jointly considering proximity to the goal and sustained progress across intermediate states. Experiments on four visual goal-reaching tasks demonstrate that ProWorld achieves an average absolute success-rate gain of 9.67 over LeWM. The code will be released after the paper is accepted.