Fréchet Distance optimized as FD-loss in representation space by decoupling population size from batch size improves generator quality, enables one-step generation from multi-step models, and motivates a multi-representation metric FDr^k.
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Generative Modeling via Drifting
24 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Generative modeling can be formulated as learning a mapping f such that its pushforward distribution matches the data distribution. The pushforward behavior can be carried out iteratively at inference time, for example in diffusion and flow-based models. In this paper, we propose a new paradigm called Drifting Models, which evolve the pushforward distribution during training and naturally admit one-step inference. We introduce a drifting field that governs the sample movement and achieves equilibrium when the distributions match. This leads to a training objective that allows the neural network optimizer to evolve the distribution. In experiments, our one-step generator achieves state-of-the-art results on ImageNet at 256 x 256 resolution, with an FID of 1.54 in latent space and 1.61 in pixel space. We hope that our work opens up new opportunities for high-quality one-step generation.
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2026 24representative citing papers
DriftXpress approximates drifting kernels via projected RKHS fields to lower training cost of one-step generative models while matching original FID scores.
W-Flow achieves state-of-the-art one-step ImageNet 256x256 generation at 1.29 FID by training a static neural network to follow a Wasserstein gradient flow that minimizes Sinkhorn divergence, delivering roughly 100x faster sampling than comparable multi-step models.
First-order asymptotic expansions of weak and Fréchet discretization errors in diffusion sampling are derived, explicit under Gaussian data through covariance geometry and robust to other data geometries.
DriftSE achieves one-step speech enhancement by evolving the pushforward distribution of a mapping function to match the clean speech distribution using a learned drifting field.
For companion-elliptic kernels vanishing drifting fields identify target measures exactly, and field convergence yields weak convergence once mass escape to infinity is detected by a single C0 scalar.
MISTY delivers state-of-the-art closed-loop scores on nuPlan Test14-hard (80.32 non-reactive, 82.21 reactive) at 10.1 ms latency via single-step MLP-Mixer inference and a latent drifting loss that encourages proactive maneuvers.
Drifting MPC produces a unique distribution over trajectories that trades off data support against optimality and enables efficient receding-horizon planning under unknown dynamics.
DFP is a one-step generative policy using Wasserstein gradient flow on a drifting model backbone, with a top-K behavior cloning surrogate, that reaches SOTA on Robomimic and OGBench manipulation tasks.
Cola DLM proposes a hierarchical latent diffusion model that learns a text-to-latent mapping, fits a global semantic prior in continuous space with a block-causal DiT, and performs conditional decoding, establishing latent prior modeling as an alternative to token-level autoregressive language model
SymDrift makes drifting models produce symmetry-invariant samples in one step via symmetrized coordinate drifts or G-invariant embeddings, outperforming prior one-shot baselines on molecular benchmarks and cutting compute by up to 40x.
Training and sampling in static scalar energy generative models are two instances of the same Lyapunov-driven density transport dynamics on Wasserstein space, differing only by initial condition, which yields a finite stopping criterion for Langevin sampling and additive composition rules that keep
ReflectDrive-2 combines masked discrete diffusion with RL-aligned self-editing to generate and refine driving trajectories, reaching 91.0 PDMS on NAVSIM camera-only and 94.8 in best-of-6.
GDM reformulates 3D conditional medical image generation as attractive-repulsive drifting with multi-level feature banks to balance distribution plausibility, patient fidelity, and one-step inference, outperforming GANs, flows, and SDEs on MRI-to-CT and sparse CT tasks.
DMF augments kernel-based drifting models with scheduled friction to guarantee convergence and matches Optimal Flow Matching on FFHQ adult-to-child translation at 16x lower training cost.
PODPO is a likelihood-free generative policy optimization method for online RL that steers actions to high-return regions using only positive-advantage samples and local contrastive drifting.
The lookahead drifting model improves upon the drifting model by sequentially computing multiple drifting terms that incorporate higher-order gradient information, leading to better performance on toy examples and CIFAR10.
Elastic Looped Transformers share weights across recurrent blocks and apply intra-loop self-distillation to deliver 4x parameter reduction while matching competitive FID and FVD scores on ImageNet and UCF-101.
Drift fields are not conservative except for Gaussian kernels; sharp normalization makes them conservative for any radial kernel by equating them to score differences of kernel density estimates.
Drifting models outperform diffusion, CNN, VAE, and GAN baselines in MRI-to-CT synthesis on two pelvis datasets with higher SSIM/PSNR, lower RMSE, and millisecond one-step inference.
MicroDiffuse3D is a foundation model that restores 3D microscopy images under sparse super-resolution, joint degradation, and low-SNR denoising, reporting 10.58% segmentation and 15.59% line-profile gains over baselines.
A consistency-regularized Euclidean-Wasserstein-2 gradient flow performs joint posterior sampling and prompt optimization in latent space for efficient low-NFE inverse problem solving with diffusion models.
A simplified one-step diffusion distillation uses pretrained teacher features directly for drifting loss plus a mode coverage term, achieving FID 1.58 on ImageNet-64 and 18.4 on SDXL.
GMD algorithms correspond to limiting points of Wasserstein gradient flows on the KL divergence with Parzen smoothing and bear resemblance to Sinkhorn divergence fixed points, with extensions to MMD and other divergences.
citing papers explorer
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Representation Fr\'echet Loss for Visual Generation
Fréchet Distance optimized as FD-loss in representation space by decoupling population size from batch size improves generator quality, enables one-step generation from multi-step models, and motivates a multi-representation metric FDr^k.
-
DriftXpress: Faster Drifting Models via Projected RKHS Fields
DriftXpress approximates drifting kernels via projected RKHS fields to lower training cost of one-step generative models while matching original FID scores.
-
One-Step Generative Modeling via Wasserstein Gradient Flows
W-Flow achieves state-of-the-art one-step ImageNet 256x256 generation at 1.29 FID by training a static neural network to follow a Wasserstein gradient flow that minimizes Sinkhorn divergence, delivering roughly 100x faster sampling than comparable multi-step models.
-
Geometry-Aware Discretization Error of Diffusion Models
First-order asymptotic expansions of weak and Fréchet discretization errors in diffusion sampling are derived, explicit under Gaussian data through covariance geometry and robust to other data geometries.
-
Speech Enhancement Based on Drifting Models
DriftSE achieves one-step speech enhancement by evolving the pushforward distribution of a mapping function to match the clean speech distribution using a learned drifting field.
-
Identifiability and Stability of Generative Drifting with Companion-Elliptic Kernel Families
For companion-elliptic kernels vanishing drifting fields identify target measures exactly, and field convergence yields weak convergence once mass escape to infinity is detected by a single C0 scalar.
-
MISTY: High-Throughput Motion Planning via Mixer-based Single-step Drifting
MISTY delivers state-of-the-art closed-loop scores on nuPlan Test14-hard (80.32 non-reactive, 82.21 reactive) at 10.1 ms latency via single-step MLP-Mixer inference and a latent drifting loss that encourages proactive maneuvers.
-
Receding-Horizon Control via Drifting Models
Drifting MPC produces a unique distribution over trajectories that trades off data support against optimality and enables efficient receding-horizon planning under unknown dynamics.
-
Drifting Field Policy: A One-Step Generative Policy via Wasserstein Gradient Flow
DFP is a one-step generative policy using Wasserstein gradient flow on a drifting model backbone, with a top-K behavior cloning surrogate, that reaches SOTA on Robomimic and OGBench manipulation tasks.
-
Continuous Latent Diffusion Language Model
Cola DLM proposes a hierarchical latent diffusion model that learns a text-to-latent mapping, fits a global semantic prior in continuous space with a block-causal DiT, and performs conditional decoding, establishing latent prior modeling as an alternative to token-level autoregressive language model
-
SymDrift: One-Shot Generative Modeling under Symmetries
SymDrift makes drifting models produce symmetry-invariant samples in one step via symmetrized coordinate drifts or G-invariant embeddings, outperforming prior one-shot baselines on molecular benchmarks and cutting compute by up to 40x.
-
Energy Generative Modeling: A Lyapunov-based Energy Matching Perspective
Training and sampling in static scalar energy generative models are two instances of the same Lyapunov-driven density transport dynamics on Wasserstein space, differing only by initial condition, which yields a finite stopping criterion for Langevin sampling and additive composition rules that keep
-
ReflectDrive-2: Reinforcement-Learning-Aligned Self-Editing for Discrete Diffusion Driving
ReflectDrive-2 combines masked discrete diffusion with RL-aligned self-editing to generate and refine driving trajectories, reaching 91.0 PDMS on NAVSIM camera-only and 94.8 in best-of-6.
-
Generative Drifting for Conditional Medical Image Generation
GDM reformulates 3D conditional medical image generation as attractive-repulsive drifting with multi-level feature banks to balance distribution plausibility, patient fidelity, and one-step inference, outperforming GANs, flows, and SDEs on MRI-to-CT and sparse CT tasks.
-
Attraction, Repulsion, and Friction: Introducing DMF, a Friction-Augmented Drifting Model
DMF augments kernel-based drifting models with scheduled friction to guarantee convergence and matches Optimal Flow Matching on FFHQ adult-to-child translation at 16x lower training cost.
-
Positive-Only Drifting Policy Optimization
PODPO is a likelihood-free generative policy optimization method for online RL that steers actions to high-return regions using only positive-advantage samples and local contrastive drifting.
-
Lookahead Drifting Model
The lookahead drifting model improves upon the drifting model by sequentially computing multiple drifting terms that incorporate higher-order gradient information, leading to better performance on toy examples and CIFAR10.
-
ELT: Elastic Looped Transformers for Visual Generation
Elastic Looped Transformers share weights across recurrent blocks and apply intra-loop self-distillation to deliver 4x parameter reduction while matching competitive FID and FVD scores on ImageNet and UCF-101.
-
Drifting Fields are not Conservative
Drift fields are not conservative except for Gaussian kernels; sharp normalization makes them conservative for any radial kernel by equating them to score differences of kernel density estimates.
-
MRI-to-CT synthesis using drifting models
Drifting models outperform diffusion, CNN, VAE, and GAN baselines in MRI-to-CT synthesis on two pelvis datasets with higher SSIM/PSNR, lower RMSE, and millisecond one-step inference.
-
MicroDiffuse3D: A Foundation Model for 3D Microscopy Imaging Restoration
MicroDiffuse3D is a foundation model that restores 3D microscopy images under sparse super-resolution, joint degradation, and low-SNR denoising, reporting 10.58% segmentation and 15.59% line-profile gains over baselines.
-
Consistency Regularised Gradient Flows for Inverse Problems
A consistency-regularized Euclidean-Wasserstein-2 gradient flow performs joint posterior sampling and prompt optimization in latent space for efficient low-NFE inverse problem solving with diffusion models.
-
Teacher-Feature Drifting: One-Step Diffusion Distillation with Pretrained Diffusion Representations
A simplified one-step diffusion distillation uses pretrained teacher features directly for drifting loss plus a mode coverage term, achieving FID 1.58 on ImageNet-64 and 18.4 on SDXL.
-
On the Wasserstein Gradient Flow Interpretation of Drifting Models
GMD algorithms correspond to limiting points of Wasserstein gradient flows on the KL divergence with Parzen smoothing and bear resemblance to Sinkhorn divergence fixed points, with extensions to MMD and other divergences.