Parametric Trajectory Distillation for Few-Step Video Generation

Lan Feng; Peter Karkus; Maximilian Igl; Julius Berner; Yuxiao Chen; Shuhan Tan; Alexandre Alahi; Boris Ivanovic

cs.CVOct 8, 2026

Parametric Trajectory Distillation for Few-Step Video Generation

Authors: Lan Feng, Peter Karkus, Maximilian Igl, Julius Berner, Yuxiao Chen, Shuhan Tan, Alexandre Alahi, Boris Ivanovic, +1 more

Organizations: EPFL · NVIDIA · Stanford University

Abstract

Video diffusion and flow models require many sequential evaluations, making generation computationally expensive. Few-step distillation reduces this cost but poses a capacity allocation problem: a student must match the teacher's iterative generation with far less sequential computation. Existing trajectory methods ask the student to reproduce teacher transitions that are highly curved at high noise, which can exceed its capacity and degrade fine detail. We introduce Parametric Trajectory Distillation (PTD), which lets the student parameterize teacher trajectory segments as polynomials and learn from teacher guidance along its own predicted path. PTD is designed to let the learned curvature adapt to the backbone's predictive capacity, preserving motion and diversity. The curvature head is used only in training; inference keeps the original backbone architecture. On Wan2.1-14B, four-step PTD sets a new state of the art for trajectory distillation, significantly improving dynamic quality and naturalness over PDD, the best-performing trajectory-only method on this model, under the same training setting. On the 33B audio-video MiniMax-H3, LoRA-trained PTD significantly improves diversity and naturalness over the state-of-the-art LightX2V Turbo. Blinded human votes give PTD 55.1% and 63.4% preference shares against PDD and LightX2V Turbo. Project page: https://alan-lanfeng.github.io/PTD/.

Figures & tables

Panel of Figure 2 — Figure 2: Parametric Trajectory Distillation. One student evaluation predicts mean velocity ${\bm{h}}$ and curve coefficients ${\bm{c}}$ for a latent denoising segment. Teacher velocities queried on the student curve train both outputs with one least-squares loss. Inference uses only ${\bm{h}}$ for the endpoint update; the curvature head is removed. Illustrative video thumbnails depict a segment ending at the data endpoint; the same construction applies between intermediate noise levels. Arrows show step-scaled velocities; two queries are the default.

Panel of Figure 3 — Figure 3: Where should the student receive teacher supervision? (a) Dense teacher integration constructs an endpoint target at the cost of many sequential evaluations; on strongly curved, high-noise hops, a limited-capacity student cannot learn this transition well, and fine detail softens. (b) PTD queries teacher velocities on the student’s current approximation, jointly training its displacement and shape through local guidance. Section 4.4 compares these supervision choices.

Panel of Figure 4 — Figure 4: PTD improves naturalness over both baselines and receives majority human preference shares. The first four rows show Astra-derived outcomes over 100 prompts, with ties split equally; dashed lines mark 50%. Outcomes use scores averaged over four calls per prompt, with differences below $0.25$ in magnitude counted as ties. Human preference is a separate holistic vote (Appendix C ). Both evaluations use H3 PTD at 150 updates and Wan PTD at 64 versus PDD at 96. Appendix Table 4 reports the automated scores.

Published reference results
Method	NFE	VBench $\uparrow$			Diversity $\uparrow$
Method	NFE	Overall	Quality	Semantic	V-JEPA 2	VideoMAE
UniPC ∗ (Teacher)	$50{\times}2$	83.90	84.56	81.24	0.1263	0.0250
rCM †	4	84.92	85.43	82.88	—	—
AnyFlow ∗	4	84.95	85.70	81.92	0.0786	0.0130
DMD2 ∗∗ (FastGen)	4	84.40	85.16	81.34	0.0568	0.0095

Table 1: VBench and diversity on Wan2.1-14B. Under the same training setting, PTD at 64 updates outperforms the best checkpoint of our PDD reproduction (96 updates) in overall, quality, and semantic VBench scores; bold compares these two rows. Gray scores are published reference results from Anonymous (2026) .

Panel of Figure 5 — Figure 5: Learning teacher-aligned curvature on Wan2.1-14B. Bend projection normalized by teacher bend energy (eight prompts). PTD learns a larger aligned component on the high-noise first hop; final-hop projections remain close. Vertical dashed lines mark 64 updates, the evaluated PTD checkpoint.

Figure 6: Student-curve supervision preserves local detail. Three Wan2.1-1.3B students after 40 training updates, all using four-step inference, shown at the same two timestamps per prompt. Teacher marching on every hop softens the dog’s coat and the painter’s hand and brush; both student-curve variants retain distinct detail. Step and query counts refer to teacher supervision per training hop.

Panel of Figure 7 — Figure 7: Two queries give a small target-estimation error. On video hops 0–2, two-query quadrature MSE is about one eighth of student MSE; three queries reduce it further. Each hop’s student MSE sets the reference scale (100%). Quadrature and student errors use separate banks of 100 and 96 prompts, respectively. Appendix D.1 gives the protocol.

Panel of Figure 8 — Figure 8: Curve capacity far exceeds what student features can predict. Offline Legendre fits (8 teacher trajectories) and final-hop linear probes (500 held-out prompts) use separate H3 banks. Solid and dashed lines denote fits and predictions, respectively. The band marks the default $K=8$ , where the Adam range spans parameterizations; probes cover $K\leq 8$ . See Appendix D.3 .

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

	Velocity target	Target query states	Student velocity	Deployed update
LMD	Frozen teacher	Predicted map states	JVP of a two-time network	Two-time map
TVM	Own EMA velocity, plus flow matching on data	Predicted terminal states	JVP of a two-time network, backpropagated	Two-time map
$\pi$ -Flow	Frozen teacher	Detached policy rollout, numerically integrated	Closed-form policy	Policy integrated with substeps
PDD	Teacher midpoint RK target	Teacher solver stages	Discrete interval outputs	Fused interval outputs
PTD	Frozen teacher	Detached student curve, in closed form	Analytic basis derivative	${\bm{x}}_{k}+\Delta_{k}{\bm{h}}_{\theta}$

Appendix

Table 2: PTD among Lagrangian and related distillation methods. LMD: Lagrangian map distillation ( Boffi et al., 2025a ; Boffi et al., 2025b ) ; TVM: Terminal Velocity Matching ( Zhou et al., 2026 ) ;

\pi

-Flow ( Chen et al., 2026 ) ; PDD ( Anonymous, 2026 ) . RK: Runge–Kutta; JVP: Jacobian–vector product. PTD’s entries describe its student-curve loss; H3’s final interval uses a teacher march instead (Appendix B.3 ).

Dimension	PTD	Baseline	$\delta$	95% CI	W/T/L
MiniMax-H3: PTD at 150 updates vs. released LightX2V Turbo v1.1
Dynamic quality	2.70	2.61	$+0.09$	$[-0.04,\,+0.21]$	45/27/28
Static quality	3.04	3.06	$-0.03$	$[-0.08,\,+0.02]$	6/86/8
Naturalness	3.09	2.98	$+0.11$	$[+0.06,\,+0.17]$	28/68/4
Diversity	2.81	1.55	$+1.26$	$[+1.15,\,+1.36]$	93/6/1
Wan2.1-14B: PTD at 64 updates vs. our PDD reproduction at 96 updates

Appendix

Table 4: GPT-6 Astra scores on 100 evaluation prompts. Mean scores on a 1–4 scale;

\delta

is the paired mean difference (PTD minus baseline), with 95% bootstrap confidence intervals over 100 prompts. Each prompt has three seeds per model and four judge calls. W/T/L gives score-derived wins, ties, and losses from PTD’s perspective.

MiniMax-H3
Prompt group	$n$	Dynamic quality	Static quality	Naturalness	Diversity
Live-action (V50)	50	$+0.07$ $[-0.09,+0.23]$	$-0.06$ $[-0.16,+0.04]$	$+0.19$ $[+0.09,+0.29]$	$+1.24$ $[+1.09,+1.39]$
Action (D50)	50	$+0.10$ $[-0.10,+0.30]$	$+0.00$ $[+0.00,+0.00]$	$+0.04$ $[+0.01,+0.07]$	$+1.28$ $[+1.12,+1.43]$
Wan2.1-14B
Live-action (V50)	50	$+0.29$ $[+0.14,+0.45]$	$+0.00$ $[-0.10,+0.10]$	$+0.19$ $[+0.06,+0.33]$	$-0.12$ $[-0.30,+0.07]$
Action (D50)	50	$+0.24$ $[+0.12,+0.38]$	$+0.01$ $[-0.06,+0.10]$	$+0.25$ $[+0.12,+0.38]$	$+0.03$ $[-0.15,+0.21]$

Appendix

Table 5: Astra results by prompt group. Mean paired differences (PTD minus baseline) with 95% bootstrap confidence intervals over prompts. H3 uses LightX2V Turbo v1.1 as the baseline; Wan compares PTD at 64 updates with our PDD reproduction at 96 updates.

Method	Updates	Overall	Quality	Semantic
PDD	64	83.29	84.43	78.71
PDD (best evaluated)	96	83.67	85.24	77.40
PDD	256	82.83	83.21	81.29
PTD (best evaluated)	64	84.57	85.44	81.10

Appendix

Table 6: Wan2.1-14B checkpoints on VBench. PDD is trained for 256 updates and evaluated at 64, 96, and 256 updates; update 96 has the highest overall score and is the best evaluated PDD checkpoint. PTD is shown at its best evaluated checkpoint, 64 updates, where it exceeds all three PDD checkpoints in overall and quality scores. Bold marks the best overall score. All use four network evaluations.

Dimension	PDD @96	PTD @64	$\delta$
Quality dimensions
Subject consistency	94.45	95.79	$+1.34$
Background consistency	95.51	96.34	$+0.83$
Temporal flickering	98.74	98.80	$+0.06$
Motion smoothness	98.86	98.37	$-0.49$
Dynamic degree	85.83	76.11	$-9.72$

Appendix

Table 7: Detailed VBench results for the best evaluated checkpoints. PDD uses update 96 and PTD update 64; both use four network evaluations. Higher is better under the VBench convention. Bold marks the higher score;

\delta

is PTD minus PDD in score points.

Subset	$n$	PTD wins	Ties	Losses	Share	Non-tie win rate	95% CI	$p$
MiniMax-H3: PTD at 150 updates vs. LightX2V Turbo v1.1
All	82	45	14	23	63.4%	66%	[54, 76]	0.010
Action (D50)	43	22	10	11	62.8%	67%	[50, 80]	0.08
Live-action (V50)	39	23	4	12	64.1%	66%	[49, 79]	0.09
Wan2.1-14B: PTD at 64 updates vs. PDD at 96 updates
All	79	33	21	25	55.1%	57%	[44, 69]	0.36

Appendix

Table 8: Human preference results.

n

counts votes. Share is PTD’s preference share with ties split equally, as in Figure 4 ; the non-tie win rate excludes ties. We report Wilson 95% confidence intervals for the non-tie win rate and two-sided exact sign-test

p

-values.

Hop	Student MSE	Two queries		Three queries
Hop	Student MSE	MSE	Relative	MSE	Relative
0	0.3346	0.04218	12.6%	0.02224	6.6%
1	0.0114	0.00155	13.6%	0.00069	6.1%
2	0.0036	0.00048	13.3%	0.00021	5.8%

Appendix

Table 9: Two- and three-query estimation errors relative to student prediction error. Video mean-velocity errors on H3 hops 0–2, normalized by the reference velocity energy.

		Hop 0				Hop 1
Updates	Method	$r$	$\cos\theta$	$q$	$r/\cos\theta$	$r$	$\cos\theta$	$q$	$r/\cos\theta$
32	PTD	0.047	0.200	0.010	0.234	0.030	0.020	0.001	1.485
	PDD	0.017	0.139	0.002	0.123	0.025	0.023	0.001	1.065
64	PTD	0.081	0.171	0.014	0.476	0.046	0.028	0.001	1.668
	PDD	0.024	0.139	0.003	0.172	0.025	0.023	0.001	1.090
96	PTD	0.113	0.182	0.021	0.621	0.058	0.031	0.002	1.879

Appendix

Table 10: Wan2.1-14B trajectory-shape probe: Hops 0 and 1. Summaries on eight VBench prompts.

r

: bend magnitude ratio;

\cos\theta

: bend-direction alignment;

q

: teacher-aligned bend projection. PTD and PDD share the listed update counts in the upper block; the final checkpoints in the lower block are unmatched.

Polynomial coordinates, $K=8$
Parameterization	$K$	$\kappa(G)\,\downarrow$	Ridge $\uparrow$	Adam $\uparrow$
Parameterization	$K$	$\kappa(G)\,\downarrow$	Ridge $\uparrow$	$10^{-3}$	$10^{-4}$
Legendre, natural scale	8	7.9	45	50	46
Legendre, unit RMS	8	6.3	45	50	48
Integrated Legendre, unit RMS	8	1.05	45	49	48
Bernstein (Bézier), unit RMS	8	792	45	50	49

Appendix

Table 12: Basis choice: conditioning and finite-budget optimization. H3 final-hop linear-probe scores (%). Natural-scale and unit-RMS Legendre coordinates are distinguished.

$K$	Legendre, unit RMS $\kappa(G)\,\downarrow$	H3 probe (%) $\uparrow$ Adam $10^{-4}$
1	1.0	39
2	1.0	40–42
3	1.6	44–48
4	2.2	45–49
8	6.3	46–49

Appendix

Table 13: Additional coefficient-count diagnostics. Population conditioning and H3 final-hop frozen-feature prediction.

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Generation in video diffusion or flow models is computationally expensive due to the slow and iterative sampling process. Current state-of-the-art (SOTA) acceleration methods heavily rely on variational score distillation (VSD) and adversarial losses to distill diffusion models into few-step generators. Albeit achieving high-quality video generation, these training losses are notoriously hard to optimize and suffer from mode collapse, leading to loss of video diversity and lack of motion. In this paper, we introduce Parallel Decoding Distillation (PDD), a simplified and scalable trajectory-based distillation method for fast inference of diffusion and flow matching models. Our architecture and training procedure are compatible with any pre-trained model and support sampling with a varying number of function evaluations (NFE). PDD accelerates generation by predicting multiple denoising steps per network evaluation. Conceptually, it learns a representation of the mean velocity without regressing its derivative using JVPs or finite-difference approximations. Our method achieves SOTA performance with 4-8 NFE on LTX-2.3 Text-to-Video/Audio, Wan 14B Text-to-Video, and Qwen-Image Text-to-Image. Moreover, PDD presents a significant improvement in generated video diversity.

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