# Modular MeanFlow: Towards Stable and Scalable One-Step Generative Modeling

arXiv: https://arxiv.org/abs/2508.17426 · HTML: https://mlsanity.com/paper/2508.17426/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 51 references that are in the map.
- First posted on arXiv 24 Aug 2025.

## Builds on (most cited first, 30 of 34)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [Fast Sampling of Diffusion Models via Operator Learning](https://mlsanity.com/paper/2211.13449/) (2022)
- [The probability flow ODE is provably fast](https://mlsanity.com/paper/2305.11798/) (2023)
- [Improving the Training of Rectified Flows](https://mlsanity.com/paper/2405.20320/) (2024)
- [Improved Analysis of Clipping Algorithms for Non-convex Optimization](https://mlsanity.com/paper/2010.02519/) (2020)
- [One-Step Diffusion Distillation through Score Implicit Matching](https://mlsanity.com/paper/2410.16794/) (2024)
- [EM Distillation for One-step Diffusion Models](https://mlsanity.com/paper/2405.16852/) (2024)
- [One-Step Diffusion Distillation via Deep Equilibrium Models](https://mlsanity.com/paper/2401.08639/) (2023)
- [Convergence Analysis of Probability Flow ODE for Score-based Generative Models](https://mlsanity.com/paper/2404.09730/) (2024)
- [Frequency-Aligned Knowledge Distillation for Lightweight Spatiotemporal Forecasting](https://mlsanity.com/paper/2507.02939/) (2025)
- [Efficient Diffusion Models: A Comprehensive Survey from Principles to Practices](https://mlsanity.com/paper/2410.11795/) (2024)
- [SepPrune: Structured Pruning for Efficient Deep Speech Separation](https://mlsanity.com/paper/2505.12079/) (2025)
- [PaGoDA: Progressive Growing of a One-Step Generator from a Low-Resolution Diffusion Teacher](https://mlsanity.com/paper/2405.14822/) (2024)
- [SGLP: A Similarity Guided Fast Layer Partition Pruning for Compressing Large Deep Models](https://mlsanity.com/paper/2410.14720/) (2024)
- [Neural Diffusion Models](https://mlsanity.com/paper/2310.08337/) (2023)
- [COMAE: COMprehensive Attribute Exploration for Zero-shot Hashing](https://mlsanity.com/paper/2402.16424/) (2024)
- [Uni-Instruct: One-step Diffusion Model through Unified Diffusion Divergence Instruction](https://mlsanity.com/paper/2505.20755/) (2025)
- [Stable Consistency Tuning: Understanding and Improving Consistency Models](https://mlsanity.com/paper/2410.18958/) (2024)
- [SRKD: Towards Efficient 3D Point Cloud Segmentation via Structure- and Relation-aware Knowledge Distillation](https://mlsanity.com/paper/2506.17290/) (2025)

## Built on by (most cited first, 8 of 8)

- [Learning Straight Flows: Variational Flow Matching for Efficient Generation](https://mlsanity.com/paper/2511.17583/) (2025)
- [Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics](https://mlsanity.com/paper/2601.22123/) (2026)
- [Gradient Shaping Beyond Clipping: A Functional Perspective on Update Magnitude Control](https://mlsanity.com/paper/2510.01578/) (2025)
- [On Variance Reduction in Learning Mean Flows](https://mlsanity.com/paper/2605.09235/) (2026)
- [CaloTrilogy: Toward a Breakthrough in One-Step, End-to-End, Physics-Guided Shower Generation for Modern Calorimeters](https://mlsanity.com/paper/2606.04165/) (2026)
- [ReSSFormer: A Recursive Sparse Structured Transformer for Scalable and Long-Context Reasoning](https://mlsanity.com/paper/2510.01585/) (2025)
- [FlowConsist: Make Your Flow Consistent with Real Trajectory](https://mlsanity.com/paper/2602.06346/) (2026)
- [MUSE: Unlocking Timestep as Native Task Steering for One-Step Dense Prediction](https://mlsanity.com/paper/2606.30370/) (2026)

## Abstract (arXiv)

One-step generative modeling seeks to generate high-quality data samples in a single function evaluation, significantly improving efficiency over traditional diffusion or flow-based models. In this work, we introduce Modular MeanFlow (MMF), a flexible and theoretically grounded approach for learning time-averaged velocity fields. Our method derives a family of loss functions based on a differential identity linking instantaneous and average velocities, and incorporates a gradient modulation mechanism that enables stable training without sacrificing expressiveness. We further propose a curriculum-style warmup schedule to smoothly transition from coarse supervision to fully differentiable training. The MMF formulation unifies and generalizes existing consistency-based and flow-matching methods, while avoiding expensive higher-order derivatives. Empirical results across image synthesis and trajectory modeling tasks demonstrate that MMF achieves competitive sample quality, robust convergence, and strong generalization, particularly under low-data or out-of-distribution settings.