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The authors formalize conditional mean collapse—where Bayes-optimal point estimates under squared loss yield invalid outputs over non-convex or disconnected target manifolds—and develop Settling, an inference operator that deterministically refines proposals toward locally stable equilibria. Backed by local convergence proofs and inexact-gradient robustness conditions for learned critics, the framework decouples proposal generation from consistency evaluation at test time. In controlled geometric diagnostics where conditional-mean prediction fails completely (0/100), Settling matches the near-perfect success of stochastic denoising (99/100) while producing substantially smoother trajectories and maintaining 94–100% robustness under initialization perturbations.
When valid solutions form disconnected manifolds, standard conditional means fail 100% of the time; deterministic equilibrium refinement recovers near-perfect validity without the trajectory jitter of stochastic diffusion.
Many learning systems return a single point estimate even when admissible outputs form disconnected or non-convex sets. Under squared loss, an ambiguous conditional distribution can therefore have a Bayes-optimal conditional mean that is invalid. We formalize this failure as conditional mean collapse and introduce Settling, an equilibrium-based inference operator that separates proposal generation, consistency evaluation, and test-time equilibrium selection. The operator treats a mean-seeking proposal as an initialization and refines it toward a locally stable configuration; conditional on initialization, refinement is deterministic. We establish exact-gradient descent, local convergence, and an inexact-gradient robustness condition relevant to learned consistency critics. In a reproducible 100-context geometric diagnostic, the mean-seeking baseline succeeds in 0/100 contexts, stochastic denoising in 100/100, and Settling in 99/100 while producing substantially lower trajectory roughness. A 1,200-run sensitivity study yields 97-100% success across obstacle-jitter ranges up to 0.20 and 94-100% across one-time initialization perturbations from 0.05 to 0.50. Cross-domain panels remain mechanism illustrations; learned high-dimensional validation remains an open empirical test.
