Use the noisy diffusion state to estimate posterior probabilities over data clusters, then route the denoising computation to one or a few cluster-specific score experts. Each expert stores a low-rank covariance or low-rank score correction, so after posterior commitment the denoiser operates at the cluster intrinsic dimension rather than ambient dimension. During the early mixing phase, retain a shared full-dimensional score or evaluate a small weighted set of experts.
Replace the standard Gaussian affine reverse step with a conditional transport kernel learned from the forward transition. Given a noisy state x_{k+1}, the model predicts a full conditional distribution for x_k using a monotone conditional CDF or an autoregressive normalizing flow. This represents multimodal and state-dependent reverse transitions that cannot be captured by a single Gaussian mean and variance.
Use the learned path only as a global proposal, then correct complete trajectories rather than endpoints. Exponentiated negative work gives self-normalized importance weights, while the same path ratio gives an independent Metropolis acceptance probability. This turns an imperfect neural sampler into an asymptotically exact sampler whenever forward and reverse path laws overlap.
Represent both endpoint distributions as Gaussian mixtures and explicitly transport their component labels along with continuous states. Use an entropic coupling between source and target components, then run a separate Gaussian bridge for every selected component pair, with covariance inflation preventing unstable Riccati or Cholesky computations.
Use an entropy-production-inspired local discrepancy between full-step and coupled half-step reverse diffusion trajectories as an adaptive error signal. The sampler takes large Euler steps where the estimated marginal mismatch is small and refines only where score variation or reverse-flow mismatch is high, targeting terminal KL rather than path-space error.
Train one denoiser only for the nonquadratic residual distribution, then modify the diffusion sampler using an analytically computed quadratic Gaussian context. Changing $K$ at inference changes the target distribution without retraining the denoiser, enabling transfer across temperatures, masses, coupling strengths, and boundary conditions whenever those changes remain quadratic.