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Understanding, Accelerating, and Improving MeanFlow Training

This paper analyzes the training dynamics of MeanFlow to reveal that instantaneous velocity must be established before learning long-interval average velocities, leading to a staged training scheme that significantly accelerates convergence and achieves state-of-the-art few-step generation quality on ImageNet.

Original authors: Jin-Young Kim, Hyojun Go, Lea Bogensperger, Julius Erbach, Nikolai Kalischek, Federico Tombari, Konrad Schindler, Dominik Narnhofer

Published 2026-05-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jin-Young Kim, Hyojun Go, Lea Bogensperger, Julius Erbach, Nikolai Kalischek, Federico Tombari, Konrad Schindler, Dominik Narnhofer

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to teach a robot how to draw a perfect picture of a cat, but you want it to do it in one single brushstroke instead of the usual hundreds of tiny, careful strokes.

This is the challenge the paper tackles. The authors are working with a method called MeanFlow, which is a new way to train AI to generate images quickly. However, they found that the original training method was a bit clumsy and slow. They analyzed why it was struggling and came up with a better "lesson plan" that makes the AI learn faster and draw better pictures.

Here is the breakdown of their discovery and solution, using simple analogies.

The Problem: Two Types of "Speed"

To understand MeanFlow, imagine the AI is learning to drive a car from a starting point (noise) to a destination (a clear image). It needs to learn two things:

Instantaneous Velocity ( $v$ ): How fast and in what direction the car should move right now, at this exact second.
Average Velocity ( $u$ ): The average speed and direction needed to get from point A to point B over a longer stretch of time.

The original MeanFlow tried to teach the AI both of these at the exact same time, with the same amount of focus, from day one. The authors found this was like trying to teach a student how to run a marathon and how to tie their shoelaces simultaneously without a clear order. It didn't work well.

The Three Big Discoveries

The authors ran experiments to see how these two "speeds" interacted. They found three key rules:

1. You must learn to walk before you run.

The Finding: The AI needs to master the "Instantaneous Velocity" (the immediate direction) first. If the AI doesn't have a solid grasp of where to move right now, it cannot learn how to plan a long trip (Average Velocity).
The Analogy: Imagine trying to teach a child how to navigate a whole city (Average Velocity) before they know how to turn left or right at a single intersection (Instantaneous Velocity). They will get lost immediately. The paper shows that if you mess up the "left/right" training, the "city navigation" training fails completely.

2. Small steps help; giant leaps hurt.

The Finding: When the AI is learning the "Average Velocity," the size of the time gap matters.
- Small Gaps: If the AI practices planning short trips (e.g., "go from here to the next block"), it actually helps it get better at the "Instantaneous Velocity" (turning left/right).
- Large Gaps: If the AI tries to plan a trip across the whole country immediately, it confuses the AI and ruins the "Instantaneous Velocity" it already learned.
The Analogy: It's like learning to swim. If you practice short strokes in the shallow end, you get better at your technique. But if you try to swim across the ocean on your very first day, you'll panic and sink your technique.

3. The Order of Operations Matters.

The Finding: The best way to train is to start with the basics (Instantaneous Velocity + Short trips), and only later introduce the long, complex trips (Long Average Velocity).
The Analogy: You wouldn't put a student in a Formula 1 car on day one. You start them in a go-kart (short gaps) to learn steering, then move to a sedan (medium gaps), and finally the race car (long gaps) once they are ready.

The Solution: A Smarter Training Schedule

Based on these discoveries, the authors designed a new training strategy that acts like a strict but helpful coach:

Phase 1: The Sprint. At the beginning of training, the AI focuses heavily on learning the "Instantaneous Velocity" and "Short trips." They use special tricks (borrowed from other AI methods) to make this happen super fast. This builds a strong foundation.
Phase 2: The Marathon. As the AI gets better, the training slowly shifts. It stops focusing so much on the tiny details and starts teaching the AI how to handle "Long trips" (large time gaps). This is the key to making the AI generate images in just one step.

The Results: Faster and Better

By following this new "lesson plan," the results were impressive:

Faster Learning: The AI reached the same quality of results in 2.5 times less time than the old method.
Better Quality: The final images were sharper and more realistic. On a standard test (ImageNet), they improved the score significantly (lower is better), getting much closer to the quality of slow, multi-step models but keeping the speed of one-step models.

Summary

The paper doesn't invent a new type of AI from scratch; it fixes the training schedule of an existing one (MeanFlow). They realized that the original method was trying to do too much too soon. By teaching the AI the basics first and gradually introducing complex tasks, they made the AI learn faster and draw better pictures.

In short: Don't try to teach the whole journey before you teach the first step. Build the foundation first, then expand the horizon.

Technical Summary: Understanding, Accelerating, and Improving MeanFlow Training

Problem Statement

MeanFlow is a stable, end-to-end training scheme designed to bridge the performance gap between multi-step diffusion models and efficient one-step (or few-step) generative models. It achieves this by jointly learning instantaneous velocity ( $v$ , the derivative at a single time point) and average velocity ( $u$ , the integral of velocity over a time interval). While MeanFlow narrows the gap between one-step and multi-step generation, its training dynamics remain poorly understood. The standard training approach applies a fixed loss function and sampling scheme throughout the entire process, ignoring the complex dependencies between the two coupled velocity fields. This naive strategy leads to computationally expensive training, slow convergence, and suboptimal generation quality, particularly for one-step inference.

Methodology

The authors propose an enhanced training strategy based on a detailed analysis of the interaction between instantaneous ( $v$ ) and average ( $u$ ) velocity learning. The method consists of two primary components:

Accelerated Instantaneous Velocity Formation:
To rapidly establish a robust foundation for $v$ , the authors adopt established acceleration techniques from diffusion training. Specifically, they employ:
- Specialized Timestep Sampling: Replacing standard uniform sampling with a custom distribution (e.g., Denoising Task Difficulty-based, DTD) to focus training on critical timesteps.
- Time-Dependent Loss Weighting: Applying weights (e.g., MinSNR) to the $v$ -loss to prioritize specific training phases.
  These techniques are applied to the instantaneous velocity term ( $L_v$ ) to ensure $v$ is well-formed early in the training process.
Progressive Average Velocity Weighting:
The authors introduce a progressive weighting scheme for the average velocity loss ( $L_u$ ) that evolves with training progress ( $s \in [0, 1]$ ).
- Early Stages: The weighting prioritizes small temporal gaps ( $\Delta t = t - r$ ). The weighting function is defined as $\beta(\Delta t, s) = 1 - s + \lambda s(1 - \Delta t)$ . At initialization ( $s=1$ ), this heavily favors small $\Delta t$ , which reinforces the formation of $v$ and prepares the model for larger gaps.
- Later Stages: As training progresses ( $s \to 0$ ), the weighting transitions to a uniform distribution across all gap lengths. This ensures the model learns accurate average velocities over large gaps, which are essential for one-step generation.

The integration respects MeanFlow's existing adaptive loss normalization, applying the new weighting schedules after the adaptive normalization step to maintain compatibility.

Key Observations and Contributions

The paper's core contribution is the empirical discovery of three critical learning dynamics that the standard MeanFlow training ignores:

Prerequisite of Instantaneous Velocity: Learning the average velocity ( $u$ ) is contingent upon a well-established instantaneous velocity ( $v$ ). If $v$ is poorly formed or corrupted (e.g., by injecting noise), $u$ -learning fails entirely. Conversely, pre-training or prioritizing $v$ significantly accelerates and stabilizes subsequent $u$ -learning.
Temporal Gap Sensitivity: The impact of $u$ $u$ -learning on $v$ $v$ depends on the temporal gap ( $\Delta t$ $Δ t$ ).
- Small $\Delta t$ : Supervision with small gaps facilitates the construction and refinement of $v$ .
- Large $\Delta t$ : Supervision with large gaps destabilizes and degrades an already trained $v$ .
- Implication: Large-gap supervision must be suppressed during early training to avoid disrupting $v$ -learning.
Task Affinity for Initialization: Task Affinity Score (TAS) analysis reveals that pre-training with small-gap $u$ -supervision creates a more favorable initialization for learning large-gap $u$ than pre-training with pure $v$ -loss. Small-gap supervision acts as a bridge, preparing the model for the challenging large-gap regime required for one-step generation.

Experimental Results

The authors evaluated their method on the ImageNet 256×256 benchmark using DiT architectures (B/4, M/2, L/2, and XL/2).

Performance Improvement: Using the same DiT-XL backbone and 240 training epochs, the proposed method reduces the 1-NFE (1 Noise Function Evaluation) FID from 3.43 (conventional MeanFlow) to 2.87, a 16% improvement. The 2-NFE FID improves from 2.93 to 2.64.
Convergence Speed: The enhanced training scheme achieves the performance of the conventional MeanFlow baseline in approximately 2.5× fewer training epochs.
Model Efficiency: The method allows a smaller backbone (DiT-L) to match the performance of the larger DiT-XL baseline trained with standard MeanFlow.
Robustness: The improvements are consistent across different Classifier-Free Guidance (CFG) configurations and model scales.
Ablation Studies: Experiments confirm that both velocity acceleration (for $v$ ) and progressive $L_u$ weighting are complementary; using both yields the best results, while using either alone provides partial gains.

Significance and Claims

The paper claims that by understanding the internal dynamics of MeanFlow—specifically the dependency of average velocity learning on a stable instantaneous velocity foundation and the destabilizing effect of large temporal gaps on early training—one can significantly improve both the efficiency and quality of few-step generative models.

The authors assert that their approach offers a practical foundation for designing efficient few-step models without requiring complex two-stage distillation pipelines or large-scale synthetic data. They conclude that high-quality, real-time generation is achievable by better coordinating the learning of coupled velocity fields, suggesting that there is still significant untapped potential in the training dynamics of current flow-based generative models.