B-DENSE: Branching For Dense Ensemble Network Supervision Efficiency

Parameter compression of class-conditional diffusion models reveals an underexplored limitation in output-level distillation: the unconditional score branch remains unsupervised, leaving the classifier-free guidance gap underdetermined in the student. This gap, amplified at every denoising step, admits degenerate solutions where both branches collapse toward identical predictions, rendering guidance ineffective despite low output-level training loss. This paper introduces DASH, a dual-branch distillation framework that independently supervises both score branches, uniquely specifying target branch outputs for each training sample through independent branch constraints, with an anchor term regularising conditional predictions toward ground-truth noise. The framework further introduces TIRT Transfer, which copies the teacher's converged per-timestep importance curriculum into the student as a frozen prior, eliminating the need to relearn it within limited distillation budgets. Experiments on CIFAR-10 and CIFAR-100 demonstrate that 5.9x compression maintains quality within 4 FID points of the teacher at 50-step DDIM sampling, considerably outperforming training from scratch with guidance fidelity well preserved. Ablation studies confirm that unconditional supervision is the dominant contribution, accounting for over 60% of total distillation gain. Curriculum transfer and anchor regularisation provide complementary benefit, together validating dual-branch constraints as empirically essential for guidance-preserving compression.

Discrete diffusion models excel at visual synthesis but rely on slow, iterative decoding. Existing single-step distillation methods attempt to bypass this bottleneck, either by training auxiliary score networks that effectively double compute, or by introducing specialized parameterizations and multi-stage pipelines that fragment optimization. In this paper, we introduce Fixed-Point Distillation (FPD), an end-to-end framework that constructs local correction targets by partially corrupting the student's one-step draft and refining it with a single teacher step. To compute the training objective in a semantically meaningful space, we lift discrete tokens into continuous features and apply a multi-bandwidth drift loss that iteratively accumulates these corrections. To backpropagate through the discrete bottleneck, we employ a straight-through estimator that feeds exact hard-sampled tokens to the teacher and decoder during the forward pass, ensuring that training and inference operate on the same codebook manifold, while routing continuous gradients back to the student logits. This fully differentiable pathway additionally accommodates an optional unconditional adversarial objective to enhance perceptual realism. Evaluations on both class- and text-conditional generation validate the effectiveness of our framework. FPD achieves competitive visual fidelity and structural alignment within a single inference step, narrowing the gap to multi-step teachers while outperforming existing discrete distillation baselines.

Diffusion Transformers (DiTs) deliver high-fidelity image and video generation, but inference requires many sequential model evaluations. Two acceleration strategies are increasingly important: model compression makes each evaluation cheaper, while adaptive inference avoids selected teacher computation through reuse, forecasting, or speculative execution. Their combination, however, is brittle: directly applying the evaluated adaptive methods to a compressed student can degrade quality, an observed failure mode we call the Combination Gap. We link this gap to a mismatch between pointwise distillation and short-horizon execution: a student trained at teacher states need not remain reliable when its own predictions are chained. We propose TamedFlow, which trains a compressed DiT for this deployed role through cross-architecture feature alignment, a near-identity Velocity Alignment Head, and randomized rollout supervision. At inference, a lightweight Learnable Trajectory Estimator routes completed drafts: accepted drafts bypass the teacher, while rejected drafts roll back and receive one teacher rescue step. Distilling DiT-XL/2 into DiT-B/2, TamedFlow reaches FID $2.58$ at $2.25\times$ measured speedup over DDIM-50 on ImageNet $256\times256$. Ablations support trajectory supervision, and routing controls favor LTE over random decisions at nearly matched latency. Evaluations on ImageNet $512\times512$, MS-COCO, and Latte/FaceForensics extend the empirical scope.