How Latent Transition Geometry Matters for Planning in World Models

World models support planning by predicting how the environment will evolve under candidate actions. In latent world models, the model is typically trained for one-step prediction, while planning typically requires repeatedly composing the learned transitions to compare candidate futures over a multi-step horizon. However, one-step latent predictive accuracy does not automatically translate to planning success. This raises a question: *what geometric properties of the learned one-step transition are useful for multi-step planning?* We study this question through an action-conditioned *transition-field* view of latent dynamics, using curvature regularization as a controlled geometric intervention. Across four continuous-control tasks, appropriately tuned regularization improves planning, while excessive regularization can sometimes be detrimental. To understand this observation, we decompose the transition field into an affine component and a residual non-affine component. We find that the curvature intervention reduces the field's sensitivity to action primarily by contracting its non-affine component. These sensitivity reductions propagate through the rollout, blurring the distinction among candidate futures and, in turn, altering the planner's decisions. Together, these results suggest that useful latent dynamics should retain sufficient action-induced predictive differences through multi-step propagation to keep candidate futures distinguishable to the planner.