Dependence-Adaptive Timestep Controller

Integrate this into the inference scheduler of a discrete diffusion model. Maintain continuous diffusion time t and a remaining error budget epsilon. At the current state x_t, run the denoiser and obtain per-position clean-token distributions q_i(b|x_t^{-i}); obtain a second set of logits q_i(b|x_t) from the ordinary full-context output or from a cached non-leave-one-out head. Compute each categorical entropy as H(q_i)=-sum_b q_i(b)log q_i(b), then calculate D_theta as the batch mean of the entropy difference in the displayed formula. Select Delta_t with the square-root controller, clipping it between Delta_min and Delta_max. A robust initial variant should smooth D_theta with an exponential moving average and limit successive step-size ratios to at most 2. Apply the corrective transition over [t-Delta_t,t], then recompute the proxy at the new state. The paper supplies the DTC-to-step-count motivation and the target error scaling; tau, clipping limits, smoothing coefficient, and whether the entropy difference should be summed or averaged must be calibrated empirically. First test on independent tokens, block-correlated binary tokens, and the two-string distribution {0^d,1^d}, where ambient dimension and intrinsic dependence can be separated. Then test a small masked language model on WikiText-103. Compare against 50- and 100-step uniform schedules and an entropy-only adaptive baseline. The expected signal is fewer Transformer evaluations at matched perplexity or total-variation error, with the largest gains on high-dimensional low-dependence data. Log D_theta and Delta_t to verify that the controller takes larger steps when cross-coordinate dependence is weak.