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
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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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cs.LG 19 cs.CV 10 stat.ML 4 cs.CL 3 cs.RO 3 eess.IV 2 cs.AI 1 cs.SD 1 math.OC 1 physics.chem-ph 1years
2026 45representative citing papers
Continuous language diffusion works by entering high-margin decoder basins where frozen T5 embeddings recover 93-96% of native decisions and linear readouts reach 97.9% agreement, implying models should be evaluated as representation-decoder systems.
CDM amortizes SMC inference for reward-tilted discrete diffusion by training a parameterized twist function on contrastive samples with closed-form kernels.
TokenDrift refines discrete diffusion language models by applying anti-symmetric drifting to soft-token features during training, yielding large reductions in generation perplexity at low NFEs.
A unified framework decomposes Wasserstein gradient flow velocity fields across f-divergences into a shared beta direction and divergence-specific weighting, enabling data-free one-step sampling.
Mean shift interacting particle systems generate weighted samples approximating expectations under unnormalized densities by minimizing MMD through normalizing-constant-invariant dynamics.
DriftXpress approximates drifting kernels via projected RKHS fields to lower training cost of one-step generative models while matching original FID scores.
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.
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.
Drift-AR achieves 3.8-5.5x speedup in AR-diffusion image models by using entropy to enable entropy-informed speculative decoding and single-step (1-NFE) anti-symmetric drifting decoding.
A new constrained gradient flow on the space of transport maps converges to the OT map and enables more stable and accurate training of convexity-constrained neural networks for learning Monge maps.
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.
IDP generates one-step robot actions by adaptively weighting a scalar potential objective using conditional expert geometry derived from local variations of observation-similar expert actions, combined with expert-proximal terminal evaluation.
Matching in semantic SSL feature space via Sinkhorn divergence enables effective one-step generation on ImageNet by inducing compact geometry for distribution matching, with training and evaluation features best kept distinct.
Drift-React produces full minimum energy pathways for reactions in a single step via SE(3) drifting fields, matching TS accuracy of iterative models with orders-of-magnitude speedup on Transition1x and Halo8 datasets.
LiFT factorizes 3D medical volume synthesis into per-slice 2D generation and inter-slice trajectory learning, using a tri-planar drifting loss for unconditional coherence and a z-context mixer for paired translation tasks.
Dual-Rate Diffusion interleaves sparse heavy context encoding with frequent light denoising to cut diffusion sampling cost by 2-4x on ImageNet while matching baseline quality and remaining compatible with distillation.
RDDM introduces a residual drifting field with attractive and repulsive forces to achieve one-step supervised denoising of low-dose CT, reporting superior PSNR, SSIM, FID of 5.87, and 15 ms inference time.
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.
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.
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.
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Continuous Language Diffusion as a Decoder-Interface Problem
Continuous language diffusion works by entering high-margin decoder basins where frozen T5 embeddings recover 93-96% of native decisions and linear readouts reach 97.9% agreement, implying models should be evaluated as representation-decoder systems.
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Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusion
CDM amortizes SMC inference for reward-tilted discrete diffusion by training a parameterized twist function on contrastive samples with closed-form kernels.
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Drifting Objectives for Refining Discrete Diffusion Language Models
TokenDrift refines discrete diffusion language models by applying anti-symmetric drifting to soft-token features during training, yielding large reductions in generation perplexity at low NFEs.
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A Unified Framework for Data-Free One-Step Sampling via Wasserstein Gradient Flows
A unified framework decomposes Wasserstein gradient flow velocity fields across f-divergences into a shared beta direction and divergence-specific weighting, enabling data-free one-step sampling.
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To discretize continually: Mean shift interacting particle systems for Bayesian inference
Mean shift interacting particle systems generate weighted samples approximating expectations under unnormalized densities by minimizing MMD through normalizing-constant-invariant dynamics.
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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.
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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.
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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.
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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.
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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.
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Drift-AR: Single-Step Visual Autoregressive Generation via Anti-Symmetric Drifting
Drift-AR achieves 3.8-5.5x speedup in AR-diffusion image models by using entropy to enable entropy-informed speculative decoding and single-step (1-NFE) anti-symmetric drifting decoding.
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Learning Monge maps with constrained drifting models
A new constrained gradient flow on the space of transport maps converges to the OT map and enables more stable and accurate training of convexity-constrained neural networks for learning Monge maps.
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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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Implicit Drifting Policy: One-Step Action Generation via Conditional Expert Geometry
IDP generates one-step robot actions by adaptively weighting a scalar potential objective using conditional expert geometry derived from local variations of observation-similar expert actions, combined with expert-proximal terminal evaluation.
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Generate in Reconstruction Space, Match in Semantic Space: Transport Geometry for One-Step Generation
Matching in semantic SSL feature space via Sinkhorn divergence enables effective one-step generation on ImageNet by inducing compact geometry for distribution matching, with training and evaluation features best kept distinct.
-
Drift-React: One-step Generation of Reaction Pathways via SE(3) Drifting Fields
Drift-React produces full minimum energy pathways for reactions in a single step via SE(3) drifting fields, matching TS accuracy of iterative models with orders-of-magnitude speedup on Transition1x and Halo8 datasets.
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LiFT: Lifted Inter-slice Feature Trajectories for 3D Image Generation from 2D Generators
LiFT factorizes 3D medical volume synthesis into per-slice 2D generation and inter-slice trajectory learning, using a tri-planar drifting loss for unconditional coherence and a z-context mixer for paired translation tasks.
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Dual-Rate Diffusion: Accelerating diffusion models with an interleaved heavy-light network
Dual-Rate Diffusion interleaves sparse heavy context encoding with frequent light denoising to cut diffusion sampling cost by 2-4x on ImageNet while matching baseline quality and remaining compatible with distillation.
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RDDM: A Residual-Driven Drifting Model for High-Fidelity Low-Dose CT Denoising
RDDM introduces a residual drifting field with attractive and repulsive forces to achieve one-step supervised denoising of low-dose CT, reporting superior PSNR, SSIM, FID of 5.87, and 15 ms inference time.
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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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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.
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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
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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.
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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
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On the Wasserstein Gradient Flow Interpretation of Drifting Models
The paper interprets GMD algorithms as limiting points of Wasserstein gradient flows on KL divergence with Parzen smoothing and on Sinkhorn divergence, while extending the approach to MMD, sliced Wasserstein, and GAN critics.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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A Unified View of Score-Based and Drifting Models
Drifting with Gaussian kernels exactly matches score-matching on smoothed distributions via Tweedie's formula, while Laplace kernels approximate this closely in high dimensions.
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Chreode: A Cell World Model for One-Step Temporal Dynamics and Perturbation Prediction
Chreode introduces a pretrained one-step dynamics model using a structured residual operator that improves perturbation prediction transfer from developmental trajectories to CRISPR data.
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Measure-to-measure Regression with Transformers
Formalizes nonlinear M2M regression and introduces transformer architectures as static maps and dynamic velocity fields between probability measures, tested on synthetic, particle, and organoid datasets.
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One-Step Distillation of Discrete Diffusion Image Generators via Fixed-Point Iteration
Fixed-Point Distillation constructs one-step correction targets for discrete diffusion generators via partial corruption and single teacher refinement, lifted into continuous features with a multi-bandwidth drift loss and straight-through estimation.
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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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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.
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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.
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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.
- Finite-Particle Convergence Rates for Conservative and Non-Conservative Drifting Models
- One-Step Generative Modeling via Wasserstein Gradient Flows
- Speech Enhancement Based on Drifting Models