# Control-Geometry Straightening for Sampling-Based Latent Planning

arXiv: https://arxiv.org/abs/2609.35603 · HTML: https://mlsanity.com/paper/2609.35603/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 17 of its 72 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

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

## Builds on (most cited first, 17 of 17)

- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [LeWorldModel: Stable End-to-End Joint-Embedding Predictive Architecture from Pixels](https://mlsanity.com/paper/2603.19312/) (2026)
- [LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristics](https://mlsanity.com/paper/2511.08544/) (2025)
- [Causal-JEPA: Learning World Models through Object-Level Latent Masking](https://mlsanity.com/paper/2602.11389/) (2026)
- [Value-guided action planning with JEPA world models](https://mlsanity.com/paper/2601.00844/) (2025)
- [Sensorimotor World Models: Perception for Action via Inverse Dynamics](https://mlsanity.com/paper/2606.20104/) (2026)
- [AdaJEPA: An Adaptive Latent World Model](https://mlsanity.com/paper/2606.32026/) (2026)
- [Predictive but Not Plannable: RC-aux for Latent World Models](https://mlsanity.com/paper/2605.07278/) (2026)
- [Delta-JEPA: Learning Action-Sensitive World Models via Latent Difference Decoding](https://mlsanity.com/paper/2606.31232/) (2026)
- [Learning Invariant Visual Representations for Planning with Joint-Embedding Predictive World Models](https://mlsanity.com/paper/2602.18639/) (2026)
- [On the Identifiability of Controlled World Models](https://mlsanity.com/paper/2607.22430/) (2026)
- [PRISM: PRior-guided Imagination Sampling in world Models](https://mlsanity.com/paper/2606.07974/) (2026)
- [Temporal-Distance JEPA: Plan-Aware Representation Learning for Latent World Model Predictive Control](https://mlsanity.com/paper/2607.25337/) (2026)
- [INTACT: Isomorphic Intent-to-Action Learning for Search-Free World Models](https://mlsanity.com/paper/2607.26056/) (2026)
- [LpWM: A Case for Sparse Representations in World Models](https://mlsanity.com/paper/2608.22764/) (2026)
- [SCALE: State-Calibrated Latent Embeddings for JEPA Planning in the Right Geometry](https://mlsanity.com/paper/2608.16287/) (2026)
- [Finite-Sample Closed-Loop Stability of Model Predictive Path Integral Control for Linear Time-Invariant Systems](https://mlsanity.com/paper/2607.04006/) (2026)

## Abstract (arXiv)

Joint-embedding predictive architectures enable planning with latent world models, but accurate transition prediction alone does not ensure that the planning objective is easy to optimize. We introduce Control-Geometry Straightening (CGS), a single auxiliary loss that learns planner-friendly representations by directly straightening control geometry for sampling-efficient planning. CGS matches pairwise cosine similarities among actions to those among corresponding latent differences only using local transitions from pixel-action pairs. The loss can be applied across world-model architectures using end-to-end learned or pretrained representations. Under linear-dynamics, our theoretical analysis connects this objective to temporal straightening and more balanced terminal-cost curvature across the full planning horizon, yielding finite-budget guarantees for MPPI, local contraction results for CEM, and convergence bounds for gradient descent. Across four control environments and multiple planners, CGS improves planning with fewer sampled candidates and refinement steps, achieving success-rate gains up to 20 and 12.6 percentage points over LeWorldModel (LeWM) and its temporal-straightening variant (LeWM+TS), respectively, with sampling-based planners using 128 candidates per update. Probes, comparisons with DINO-WM architecture, and planner-side ablations clarify how latent motion organization, state dependence, and dynamical context shape planning behavior. Straightening control geometry thus makes good action sequences easier to find under limited planning budgets.