Continuous-space reasoning methods replace discrete intermediate tokens with probability-weighted soft embeddings, aiming to preserve semantic information that greedy Chain-of-Thought decoding discards. We show that this promise is limited by local representation geometry and the latent semantic manifold. When the next-token distribution is low-entropy and concentrated, a soft token becomes nearly collinear with the Top-1 embedding and collapses toward greedy decoding. When the distribution is high-entropy, diffuse, or stochastically perturbed, the continuous state may leave the greedy path but drift away from the local scale of naturally occurring candidate representations. We diagnose these two regimes with step-level probes over representation divergence, local norm calibration, and behavior-cloud membership. To address them, we propose Manifold Thinking, a training-free inference framework that combines structured tangent movement away from the Top-1 direction with local norm-calibrated projection back to the candidate-token neighborhood. Across mathematical and programming benchmarks, Manifold Thinking improves over discrete CoT baselines and baselines covering the latest stochastic Soft Thinking strategies, suggesting that useful continuous reasoning requires geometric correction rather than unconstrained linear token mixing alone.