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arxiv: 2605.23381 · v1 · pith:KREE7F5Snew · submitted 2026-05-22 · 💻 cs.CV

VDE: Training-Free Accelerating Rectified Flow Model via Velocity Decomposition and Estimation

Junwen Tan , Jinglin Liang , Hongyuan Chen , Shuangping Huang This is my paper

Pith reviewed 2026-05-25 04:55 UTC · model grok-4.3

classification 💻 cs.CV
keywords rectified flow modelstraining-free accelerationvelocity decompositioninference optimizationimage generationvideo generationgenerative modelsdenoising acceleration
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The pith

VDE accelerates rectified flow models by decomposing velocity into parallel and orthogonal components to the input for estimation without training.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents Velocity Decomposition and Estimation (VDE) to speed up inference in rectified flow models for image and video generation. Prior methods cache and reuse features from earlier steps, but these caches mismatch as the input changes during generation. VDE instead splits the velocity output into parts aligned with and perpendicular to the current input, using their observed predictability over time and stable directions to estimate future values adaptively. Full model passes are inserted periodically to reset accumulated errors. Experiments show this yields speedups such as 3.22 times on Flux with an LPIPS of 0.069 on Qwen-Image, better than prior baselines.

Core claim

VDE decomposes the model's velocity into components parallel and orthogonal to the input, exploits their temporal predictability and directional stability for precise input-adaptive estimation without training, and inserts periodic full forward passes to anchor the state and prevent error accumulation, enabling faster inference in rectified flow models while preserving output fidelity.

What carries the argument

Decomposition of velocity into input-parallel and input-orthogonal components, estimated from their temporal predictability and directional stability with periodic anchoring via full passes.

If this is right

  • Rectified flow models achieve multi-fold inference speedup on image and video tasks with only minor quality degradation measured by LPIPS.
  • No model retraining or fine-tuning is required to apply the acceleration.
  • The approach outperforms feature-caching baselines by reducing the mismatch between cached states and evolving inputs.
  • Periodic full passes limit error growth, allowing longer acceleration sequences without collapse in fidelity.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same decomposition principle could be tested on non-rectified diffusion models to check if parallel-orthogonal stability generalizes.
  • Measuring how the angle between velocity and input evolves across steps might yield a diagnostic for when estimation remains reliable.
  • Applying VDE to conditional generation with text or layout inputs could reveal whether the stability holds under stronger guidance.

Load-bearing premise

The velocity components parallel and orthogonal to the input possess temporal predictability and directional stability that permit accurate estimation from prior steps without training.

What would settle it

Compare the true velocity vectors computed by the full model against VDE's estimated vectors at multiple denoising steps on the same input sequence; large consistent deviations would cause visible quality loss.

Figures

Figures reproduced from arXiv: 2605.23381 by Hongyuan Chen, Jinglin Liang, Junwen Tan, Shuangping Huang.

Figure 1
Figure 1. Figure 1: Qualitative comparison between VDE and standard 50-step sampling across Flux, Qwen-Image, and Wan2.1. VDE achieves [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison between standard feature caching and our VDE. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Temporal dynamics of velocity components. Evolution of the decomposed velocity components across Flux, Qwen-Image, and Wan2.1. Top: The parallel (αt) and orthogonal (βt) coefficients. Bottom: The cosine similarity of adjacent orthogonal directions (ut). After an initial warm-up phase (shaded), the scalar coefficients evolve smoothly with strong local linearity, while the orthogonal direction remains highly… view at source ↗
Figure 4
Figure 4. Figure 4: Quantitative evidence for the temporal regularities. We [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Qualitative comparison of caching-based methods and our VDE on Flux. VDE preserves both global structure and fine details. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Qualitative comparison of caching-based methods and our VDE on Flux, Qwen-Image, and Wan2.1. VDE successfully acceler [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
read the original abstract

Though rectified flow models have achieved remarkable performance in image, video, and 3D generation, their practical deployments are challenged by slow inference speeds. Prior acceleration methods reuse cached features from previous steps, which neglects the growing mismatch between static caches and the evolving input, leading to reduced output fidelity. This work proposes Velocity Decomposition and Estimation (VDE), a training-free acceleration method that shifts the paradigm from caching-and-reusing to decomposing-and-estimating. Specifically, VDE decomposes the model's velocity into components parallel and orthogonal to the input, exploiting their temporal predictability and directional stability for precise, input-adaptive estimation. To prevent error accumulation, it periodically anchors the model's state via full forward passes. Extensive experiments on image and video generation tasks demonstrate that VDE achieves substantial acceleration with minimal loss in visual quality. Notably, VDE accelerates Flux by 3.22 times and achieves an LPIPS of 0.069 on Qwen-Image, outperforming the best baseline with a 52.2% reduction.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes Velocity Decomposition and Estimation (VDE), a training-free acceleration technique for rectified flow models. It decomposes the velocity into components parallel and orthogonal to the input x, estimates future values from claimed temporal predictability and directional stability of those components, and periodically performs full forward passes to reset state and limit error accumulation. Experiments on image and video tasks report speedups including 3.22× on Flux and LPIPS=0.069 on Qwen-Image, outperforming baselines by 52.2%.

Significance. If the predictability and stability properties of the decomposed velocity components can be rigorously established, the method would offer a practical training-free route to faster inference in large rectified-flow models while preserving output fidelity, which is valuable for deployment in image and video generation pipelines.

major comments (2)
  1. [Abstract / method description] Abstract and method description: the central claim that the parallel and orthogonal velocity components possess 'temporal predictability and directional stability' permitting accurate input-adaptive estimation is asserted without derivation, bound, or analysis showing why these properties hold across denoising steps or different rectified-flow models. This assumption is load-bearing for the training-free estimation step and error-control argument.
  2. [Experiments] Experiments section: no ablation studies, error analysis, or protocol details are supplied to isolate whether the reported 3.22× speedup on Flux and LPIPS=0.069 on Qwen-Image arise from the decomposition/estimation or from the periodic full passes and other implementation choices. This prevents verification that the quantitative gains support the core claim.
minor comments (2)
  1. [Method] Notation for the parallel/orthogonal decomposition (v_∥ and v_⊥) should be introduced with an explicit equation early in the method section for clarity.
  2. [Abstract / Experiments] The abstract mentions 'extensive experiments on image and video generation tasks' but does not list the exact models, datasets, or metrics used beyond the two highlighted examples; a table summarizing all evaluated settings would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and commit to revisions that strengthen the presentation without altering the core claims.

read point-by-point responses

  1. Referee: [Abstract / method description] Abstract and method description: the central claim that the parallel and orthogonal velocity components possess 'temporal predictability and directional stability' permitting accurate input-adaptive estimation is asserted without derivation, bound, or analysis showing why these properties hold across denoising steps or different rectified-flow models. This assumption is load-bearing for the training-free estimation step and error-control argument.

    Authors: We agree that the manuscript motivates the properties of temporal predictability and directional stability from the structure of rectified flows but does not supply a formal derivation or bounds. The decomposition follows directly from projecting the velocity onto the input direction and its orthogonal complement, and the stability arises because the parallel component tracks the data manifold while the orthogonal tracks residual noise. In revision we will add a short analysis subsection with (i) a Lipschitz-based argument on why the components evolve more slowly than the full velocity and (ii) empirical plots of component-wise change across steps and models to support the estimation procedure. revision: yes

  2. Referee: [Experiments] Experiments section: no ablation studies, error analysis, or protocol details are supplied to isolate whether the reported 3.22× speedup on Flux and LPIPS=0.069 on Qwen-Image arise from the decomposition/estimation or from the periodic full passes and other implementation choices. This prevents verification that the quantitative gains support the core claim.

    Authors: We concur that the current experiments do not fully isolate the contribution of the decomposition-and-estimation step from the periodic anchoring. In the revised version we will add (i) an ablation that disables the adaptive estimation while retaining anchoring, (ii) per-step error curves (L2 velocity error and LPIPS) with and without anchoring, and (iii) explicit protocol details on anchoring frequency, estimation horizon, and implementation choices. These additions will allow readers to attribute the reported speed-ups and fidelity metrics to the proposed VDE components. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation rests on stated velocity properties without reduction to fitted inputs or self-citations.

full rationale

The paper's core step decomposes velocity into parallel/orthogonal components to the input and estimates future values from claimed temporal predictability and directional stability. This is presented as an exploitation of inherent rectified-flow properties rather than any fitted parameter, self-referential prediction, or load-bearing self-citation. No equations reduce the estimation to the inputs by construction, and the training-free framing avoids any internal fitting loop. The provided text contains no self-citations or ansatz smuggling that would trigger the enumerated patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract alone; the central claim rests on the unverified assumption that parallel and orthogonal velocity components exhibit the required predictability and stability, but no explicit free parameters, axioms, or invented entities are enumerated in the provided text.

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