Strong Stochastic Flow Maps learn the strong solution map of additive-noise SDEs via a pathwise-convergent polynomial Brownian approximation, generalizing deterministic flow maps and enabling simulation-free training that outperforms prior weak-convergence stochastic methods on image generation and
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Improved Mean Flows: On the Challenges of Fastforward Generative Models
28 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
MeanFlow (MF) has recently been established as a framework for one-step generative modeling. However, its ``fastforward'' nature introduces key challenges in both the training objective and the guidance mechanism. First, the original MF's training target depends not only on the underlying ground-truth fields but also on the network itself. To address this issue, we recast the objective as a loss on the instantaneous velocity $v$, re-parameterized by a network that predicts the average velocity $u$. Our reformulation yields a more standard regression problem and improves the training stability. Second, the original MF fixes the classifier-free guidance scale during training, which sacrifices flexibility. We tackle this issue by formulating guidance as explicit conditioning variables, thereby retaining flexibility at test time. The diverse conditions are processed through in-context conditioning, which reduces model size and benefits performance. Overall, our $\textbf{improved MeanFlow}$ ($\textbf{iMF}$) method, trained entirely from scratch, achieves $\textbf{1.72}$ FID with a single function evaluation (1-NFE) on ImageNet 256$\times$256. iMF substantially outperforms prior methods of this kind and closes the gap with multi-step methods while using no distillation. We hope our work will further advance fastforward generative modeling as a stand-alone paradigm.
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2026 28representative citing papers
FMRG reformulates guidance as deterministic optimal control, deriving a single-trajectory method using the flow map that matches or exceeds baselines on reward-guided generation and inverse problems with 3 NFEs at text-to-image scale.
FAV aligns few-step generative models by amortizing SVGD updates from reward-tilted sampling into generator parameters via fixed-point regression, requiring only sample access, and shows outperformance on robotics tasks plus scaling on image generators.
Discrete MeanFlow parameterizes CTMC conditional transition kernels with a boundary-by-construction design to enable exact one-step generation in discrete state spaces.
CoFlow achieves state-of-the-art coordination in offline MARL using single-pass joint velocity fields with Coordinated Velocity Attention and Adaptive Coordination Gating.
DriftSE achieves one-step high-fidelity speech enhancement by formulating denoising as an equilibrium problem solved via a drifting field that matches pushforward distributions to the clean speech distribution.
Generalizes MeanFlow to learn finite-horizon minimum-energy control coefficients for linear swarm systems via a differential identity and stop-gradient regression objective.
Matched benchmarking reveals FID misleads in few-step regimes under CFG, prompting CLIP-scaled and PickScore-scaled FID and IS variants for better semantic evaluation of one-step image generators.
RMMD simultaneously distills diffusion models and optimizes rewards, yielding better FID-reward trade-offs on ImageNet than DI++, DRaFT and HyperNoise, and a 7.5x faster GenCast model that beats its teacher on 93% of weather variables while improving calibration.
NanoGen unifies DiT training on ImageNet and T2I, reveals negative Pearson correlations (-0.377 to -0.580) in method rankings across metrics from 21 models, and motivates DiffusionBench for holistic evaluation.
NullFlow learns the average velocity of a flow confined to a measurement-consistent subspace, yielding a one-step posterior sampler whose global minimizer is proved to exist.
DeCAF distills all-atom cofolding diffusion models into few-step flow maps, showing improved or matched accuracy on protein-ligand tasks with 5x fewer inference steps.
RiskFlow is a closed-loop multi-agent traffic generation framework that uses action-space transport with a JVP-based objective to produce realistic safety-critical scenarios faster than diffusion models.
A one-step generative model for calorimeter showers, using MeanFlow, a learned Gaussian-mixture prior, and a physics-constrained loss, matches diffusion-model quality at far fewer evaluations.
CAT achieves FID-50K of 1.56 on ImageNet-256 with one-step inference after 60 epochs by aligning intermediate GAN outputs to the final sample.
MIND integrates discrete patch tokenization into diffusion score functions via soft top-k and dual-branch layers, achieving FID 22.73 (no guidance) and 2.06 (with guidance) on ImageNet-256 after 80 epochs, outperforming DiT and larger LlamaGen models.
Decouples Sphere Encoder into fixed pretrained encoder and spherical latent denoiser, yielding higher quality and faster inference than the joint original on Animal-Faces, Oxford-Flowers and ImageNet-1K.
W-Flow compresses a Wasserstein gradient flow defined via Sinkhorn divergence into a single-step neural generator, reporting 1.29 FID on ImageNet 256x256 with improved mode coverage.
ELF applies continuous-time flow matching in embedding space for language generation and reports outperforming prior discrete and continuous diffusion language models with fewer steps.
Cumulative flow maps unify few-step generative modeling for diffusion and flow models via cumulative transport and parameterization with minimal changes to time embeddings and objectives.
Point-MF performs one-step point cloud reconstruction from single images by learning a mean velocity field in point space with a tailored Diffusion Transformer and a new auxiliary loss.
FlowLM converts diffusion LMs to flow matching via fine-tuning, achieving few-step generation that rivals or beats 2000-step diffusion and saturates faster than training flow models from scratch.
Continuous flows on token embeddings with flow-map distillation produce one-step language models whose quality exceeds recent 8-step discrete diffusion baselines on LM1B and OpenWebText.
Trajectory Forcing makes generative image synthesis trajectory-centric by organizing it into decodable semantic stages derived from clustered visual representations and trained with one-step flow-matching models.
citing papers explorer
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Strong Stochastic Flow Maps
Strong Stochastic Flow Maps learn the strong solution map of additive-noise SDEs via a pathwise-convergent polynomial Brownian approximation, generalizing deterministic flow maps and enabling simulation-free training that outperforms prior weak-convergence stochastic methods on image generation and
-
How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidance
FMRG reformulates guidance as deterministic optimal control, deriving a single-trajectory method using the flow map that matches or exceeds baselines on reward-guided generation and inverse problems with 3 NFEs at text-to-image scale.
-
Aligning Few-Step Generative Models by Amortizing Sample-based Variational Inference
FAV aligns few-step generative models by amortizing SVGD updates from reward-tilted sampling into generator parameters via fixed-point regression, requiring only sample access, and shows outperformance on robotics tasks plus scaling on image generators.
-
Discrete MeanFlow: One-Step Generation via Conditional Transition Kernels
Discrete MeanFlow parameterizes CTMC conditional transition kernels with a boundary-by-construction design to enable exact one-step generation in discrete state spaces.
-
CoFlow: Coordinated Few-Step Flow for Offline Multi-Agent Decision Making
CoFlow achieves state-of-the-art coordination in offline MARL using single-pass joint velocity fields with Coordinated Velocity Attention and Adaptive Coordination Gating.
-
Speech Enhancement Based on Drifting Models
DriftSE achieves one-step high-fidelity speech enhancement by formulating denoising as an equilibrium problem solved via a drifting field that matches pushforward distributions to the clean speech distribution.
-
Learning Sampled-data Control for Swarms via MeanFlow
Generalizes MeanFlow to learn finite-horizon minimum-energy control coefficients for linear swarm systems via a differential identity and stop-gradient regression objective.
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Setting-Matched and Semantics-Scaled Benchmarking of One-Step Generative Models Against Multistep Diffusion and Flow Models
Matched benchmarking reveals FID misleads in few-step regimes under CFG, prompting CLIP-scaled and PickScore-scaled FID and IS variants for better semantic evaluation of one-step image generators.
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Diffusion Fine-tuning with Rewarded Moment Matching Distillation
RMMD simultaneously distills diffusion models and optimizes rewards, yielding better FID-reward trade-offs on ImageNet than DI++, DRaFT and HyperNoise, and a 7.5x faster GenCast model that beats its teacher on 93% of weather variables while improving calibration.
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DiffusionBench: On Holistic Evaluation of Diffusion Transformers
NanoGen unifies DiT training on ImageNet and T2I, reveals negative Pearson correlations (-0.377 to -0.580) in method rankings across metrics from 21 models, and motivates DiffusionBench for holistic evaluation.
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NullFlow: One-Step Generative Reconstruction
NullFlow learns the average velocity of a flow confined to a measurement-consistent subspace, yielding a one-step posterior sampler whose global minimizer is proved to exist.
-
Few-step Cofolding with All-Atom Flow Maps
DeCAF distills all-atom cofolding diffusion models into few-step flow maps, showing improved or matched accuracy on protein-ligand tasks with 5x fewer inference steps.
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RiskFlow: Fast and Faithful Safety-Critical Traffic Scenario Generation
RiskFlow is a closed-loop multi-agent traffic generation framework that uses action-space transport with a JVP-based objective to produce realistic safety-critical scenarios faster than diffusion models.
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CaloTrilogy: Toward a Breakthrough in One-Step, End-to-End, Physics-Guided Shower Generation for Modern Calorimeters
A one-step generative model for calorimeter showers, using MeanFlow, a learned Gaussian-mixture prior, and a physics-constrained loss, matches diffusion-model quality at far fewer evaluations.
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Cross-scale Aligned Supervision for Training GANs
CAT achieves FID-50K of 1.56 on ImageNet-256 with one-step inference after 60 epochs by aligning intermediate GAN outputs to the final sample.
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Diffusion Image Generation with Explicit Modeling of Data Manifold Geometry
MIND integrates discrete patch tokenization into diffusion score functions via soft top-k and dual-branch layers, achieving FID 22.73 (no guidance) and 2.06 (with guidance) on ImageNet-256 after 80 epochs, outperforming DiT and larger LlamaGen models.
-
Efficient Image Synthesis with Sphere Latent Encoder
Decouples Sphere Encoder into fixed pretrained encoder and spherical latent denoiser, yielding higher quality and faster inference than the joint original on Animal-Faces, Oxford-Flowers and ImageNet-1K.
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One-Step Generative Modeling via Wasserstein Gradient Flows
W-Flow compresses a Wasserstein gradient flow defined via Sinkhorn divergence into a single-step neural generator, reporting 1.29 FID on ImageNet 256x256 with improved mode coverage.
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ELF: Embedded Language Flows
ELF applies continuous-time flow matching in embedding space for language generation and reports outperforming prior discrete and continuous diffusion language models with fewer steps.
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A Few-Step Generative Model on Cumulative Flow Maps
Cumulative flow maps unify few-step generative modeling for diffusion and flow models via cumulative transport and parameterization with minimal changes to time embeddings and objectives.
-
Point-MF: One-step Point Cloud Generation from a Single Image via Mean Flows
Point-MF performs one-step point cloud reconstruction from single images by learning a mean velocity field in point space with a tailored Diffusion Transformer and a new auxiliary loss.
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FlowLM: Few-Step Language Modeling via Diffusion-to-Flow Adaptation
FlowLM converts diffusion LMs to flow matching via fine-tuning, achieving few-step generation that rivals or beats 2000-step diffusion and saturates faster than training flow models from scratch.
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Flow Map Language Models: One-step Language Modeling via Continuous Denoising
Continuous flows on token embeddings with flow-map distillation produce one-step language models whose quality exceeds recent 8-step discrete diffusion baselines on LM1B and OpenWebText.
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Trajectory Forcing: Structure-First Generation with Controllable Semantic Trajectories
Trajectory Forcing makes generative image synthesis trajectory-centric by organizing it into decodable semantic stages derived from clustered visual representations and trained with one-step flow-matching models.
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Mean Flow Distillation: Robust and Stable Distillation for Flow Matching Models
Mean Flow Distillation distills flow matching models to single-step generation by proving that matching expected average velocities suffices for distribution alignment and acts as a temporal low-pass filter to stabilize training.
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Drift Flow Matching
Drift Flow Matching connects direct transport maps from Drift Models with flow-based iterative refinement to enable adaptive computation in generative modeling.
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Real-time Speech Restoration using Data Prediction Mean Flows
A Data Prediction Mean Flow model enables real-time speech restoration with 120x lower compute and no algorithmic latency beyond the STFT while matching state-of-the-art offline quality.
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Accelerating Redshift-Conditioned Galaxy Image Synthesis with One-step Generative Modeling
One-step pixel-MeanFlow models recover key galaxy morphology statistics at orders-of-magnitude lower computational cost than standard DDPM sampling while remaining weaker on fine-grained structure.