VA-TDM: A Unified View for Improving Few-Step Diffusion Models by Velocity Adversarial Distillation

VA-TDM uses an adversarial velocity-field framework to distill diffusion and flow models into high-quality four-step generators.

Few-step distillation must replace a long teacher trajectory with a few student transitions while preserving generation quality. Distribution-matching methods via score distillation depend on accurately tracking the student's changing distribution. At intermediate student steps, student-score estimation is difficult, and common estimators may describe a different distribution from the one used to update the student.

The paper introduces Velocity Adversarial Distillation, which constructs student velocity fields from the student sampling process and uses a vector-valued critic to compare student and teacher velocity fields. The optimal critic is the velocity residual, and the adversarial game has a matching equilibrium where student and teacher velocities agree. Two velocity constructions are derived: A-form, a rectified velocity tied to the conditional clean-prediction moment, and B-form, a Gaussian velocity tied to the score of the perturbed student distribution. The framework connects these forms and generator updates to score distillation, Fisher-based matching, moment matching, and MMD. VA-TDM applies the framework along the student trajectory, combines A-form and B-form games with a shared backbone, uses transition-aware field estimation, and initializes with on-trajectory ODE regression warm-up.

• On SD3.5-Medium, VA-TDM raises GenEval from TDM's 0.61 to 0.67 and reaches OCR 0.59 while leading compared few-step models on verifiable, quality, and preference metrics. §4.1
• On FLUX.2-Klein-Base 4B, VA-TDM raises GenEval from 0.78 to 0.80, OCR similarity from 0.64 to 0.69, and LPIPS diversity from 0.47 to 0.56. §4.1
• In the video user study, VA-TDM wins 61.33% of comparisons against Fast-H3 at the same 4-NFE budget and achieves a 45.53% preference rate against the 100-NFE teacher, compared with 24.67% for Fast-H3. §1
• The final four-step SD3.5-Medium ablation configuration with lambda_m=0.8, path/flow-product mixing, field regularization, and the regularization-corrected critic reaches GenEval 0.67, OCR 0.59, Aesthetic 5.65, ImageReward 1.02, PickScore 0.8702, HPSv2 0.3010, HPSv3 11.89, and LPIPS 0.58. §4.2
• Removing transition-aware field estimation in the B-form-only setting lowers GenEval from 0.61 to 0.58, OCR from 0.57 to 0.53, and LPIPS from 0.59 to 0.56. §4.2

• The paper reports unstable training and collapse when gradients are propagated through the critic output, so the practical update stops the entire critic output; this is stated in the method and shown in Fig. 2.
• The B-form alone induces high-variance online field learning and is difficult to learn on its own, motivating the shared backbone and dual-form mixing; this is stated in the ablation discussion.
• The experiments distill SD3.5-Medium, FLUX.2-Klein-Base 4B, and MiniMax-H3 into four-step generators, so behavior at other step budgets is left open by the reported experiments.
• The MiniMax-H3 user study uses 10 randomly chosen prompts, so the human evaluation is limited in scale; this is stated in the experimental details.

• VAD defines an adversarial game where a vector-valued critic compares student and teacher velocity fields through inner products. §3.2
• For a fixed student, the optimal critic is the teacher velocity minus the student marginal velocity. §3.2
• A-form rectified velocity is an affine reparameterization of the conditional clean-prediction moment and produces reduced training variance when s>0. §3.1
• B-form Gaussian velocity is an affine reparameterization of the score of the actual perturbed student distribution. §3.1
• Theorem 5 links A-form matching to conditional-moment matching and B-form matching to distribution matching, and links generator updates to MMD, reverse-KL, and Fisher divergence. §3.2
• VA-TDM optimizes the A-form and B-form adversarial games with a shared backbone and separate output heads. §3.3
• Transition-aware field estimation injects the target timestep of the student transition as extra input to the online velocity field. §3.3
• Training uses LoRA fine-tuning with rank 64 and updates the online score and generator once each iteration. §C.1