Flow-Efficiency Drift Scheduler

1. Integration point: place this controller around the conditional-flow sampler used for diffusion sampling, neural energy models, Bayesian neural networks, or world-model trajectory distributions. Store each proposal's flow log density, prior log density, constraint result, and score. 2. Pseudocode: after every nested level, compute normalized ESS from importance weights; evaluate both $q_i(x)$ and $q_{i-1}(x)$ on a small proposal buffer to estimate symmetric KL drift; if $D_i^{\mathrm{sym}}>D_{\max}$, discard old examples, halve the FIFO window $K$, and perform additional flow updates; if $\eta_i<\eta_{\min}$ while drift is small, increase $R_i$ and apply 5 to 20 local HMC or Langevin correction steps; if efficiency remains high for several levels, enlarge $K$ and reduce updates. Flag a level when ESS is below 1% of proposals. 3. The paper supplies the mechanism that efficiency varies non-monotonically along annealing and becomes poor in internally complex liquid-like ensembles. Thresholds, window limits, and fallback lengths must be estimated in a pilot run. 4. First experiment: use a 16-dimensional mixture of eight Gaussians with controllable separation and threshold drift. Compare fixed-window flow sampling with the adaptive controller. Prediction: under rapidly changing targets, adaptation keeps $\eta_i\ge0.1$ by shortening $K$, whereas fixed-window training falls below $0.02$. In a dense multimodal interval, efficiency should show a reproducible local minimum; the controller should increase compute there while preserving evidence accuracy. Verify that log-evidence error remains stable when the fixed-window baseline suffers ESS collapse.