PDMD: Projected Distribution Matching Distillation for Video Diffusion Models

What it claims

DMD's oversaturation and texture drift come from the online critic's errors being fed into each student update. The paper identifies a quantity DMD already computes that estimates this error: the residual between the critic's one-step denoised endpoint and the student sample. PDMD removes the part of the DMD update that points along that residual. It adds no loss, network, model pass, data or training stage, and critic training is unchanged.

Models tested:

• Wan2.1-T2V-1.3B, distilled to 4 NFE.
• MiniMax-H3-33B, joint video–audio, producing 14.4 s, 1366×768 clips at 4 NFE.

How it works

The paper's student step, with the projection as the only change from DMD:

x_0_s = G(z, cond)
x_t, t = renoise(x_0_s) # Eq. (1)
s_t = T.score(x_t, t, cond)
s_c, x_0_c = C.score_end(x_t, t, cond)
d = s_c - s_t # Eq. (2)
r = x_0_c - x_0_s
d = d - dot(d, r) / dot(r, r) * r # Eq. (4)
update(G, dmd_loss(x_0_s, d))

Implementation details:

• The critic endpoint comes from the critic score with no extra pass: x_0_c = (x_t + σ_t² · s_critic) / α_t.
• When r = 0, the update is left unchanged.

Why the residual is the right direction:

• At a fixed noisy query, r is an unbiased estimate of the critic's endpoint error.
• The expected fraction of error energy removed is at least ‖e‖² / (‖e‖² + tr Σ(q)), where Σ(q) is the covariance of student endpoints given the query. For example, when the two terms are equal, at least 50% of the error is removed.
• The claim that only a vanishing fraction of the true DMD signal is lost depends on two assumptions: high-dimensional concentration, and no dominant alignment between the noise and the error direction.

Evidence

Wan2.1-T2V-1.3B, 4 NFE, VBench (AnyFlow protocol):

User studies (PDMD win minus loss) favour PDMD on visual quality (+24.0 to +53.6) and motion (+17.7 to +35.2) against every baseline.

MiniMax-H3:

• VideoGen-Eval visual total is 83.17, 0.41 above the strongest distilled baseline.
• PDMD has the best score on all six audio metrics among 4-NFE models.
• DMD is visibly oversaturated from about 500 iterations onward.
• The projection keeps more than 80% of the update norm for most of training (83% in the illustrated example).

2D toy experiments (exact teacher, so the critic is the only learned score):

• On a ring of eight Gaussians, the paper tested projecting out other directions: a random direction, the critic score, and the teacher endpoint residual. These removed a similar share of the update norm, but only the critic-endpoint residual improved both energy distance and on-mode fraction over DMD.
• PDMD cut the mean squared error to the ideal update by 28% for σ ∈ [0.15, 1.1].
• On a two-mode target with the critic learning rate at 1/20 of the student's, PDMD collapsed in 3/20 runs versus 14/20 for DMD.

How to use it

Code and models are linked from https://pdmd2026.github.io/, which also links GitHub and Hugging Face. If you already run DMD, adoption is the single projection line above. The fetched text states no licence.

Limits

• Theory: the guarantee of discarding little true signal holds only under the high-dimensional and weak-alignment assumptions. The unbiasedness result is per fixed query.
• Semantic and text alignment:
• PDMD's VBench Semantic score (75.09) is below AnyFlow (76.57) and the 50-step teacher (75.23).
• In the text-alignment user study, PDMD is roughly even with the other methods (−2.1 to +7.5) and slightly loses to rCM (−2.1) and the teacher (−0.4). The gains are concentrated in visuals and motion.
• Baselines: DMD and DMD2 are the authors' best reimplemented checkpoints, not official releases.
• Missing data: MiniMax-H3 results beyond the headline numbers (Table 2) and the rest of the paper were not in the fetched text.