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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2026 54representative citing papers
Uniform-in-time propagation-of-chaos bounds for SVGD are obtained via cutoff for distributional metrics (logarithmic rates) and via finite-dimensional closure plus conjugacy for Gaussian targets (parametric N^{-1/2} rates).
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.
DrPO enables online preference optimization for deterministic one-step generators via non-parametric dipole updates from ranked samples plus base-model drift, without reward backpropagation.
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.
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.
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.
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.
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.
Pepti-drift performs a single antigen-conditioned drift in peptide latent space to produce valid, diverse peptides with reduced toxicity and high efficiency compared to prior methods.
Lifts CCCP to Wasserstein space for DC functionals on measures, proves almost stationarity under smoothness/strong-convexity assumptions, and applies to MMD/ED with local convergence and faster empirical runs.
A label-conditioned drifting model in VAE latent space matches diffusion accuracy for flow surrogates while running two orders of magnitude faster, with a spatial variant for unseen geometries.
Clari, a unit-cell flow matching model with pair-bias attention, generates organic crystal structures faster than OXtal while improving solve rates and supporting energy-based ranking without relaxation.
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.
Derives continuous-time finite-particle convergence rates for a new conservative KDE-gradient drifting method and the non-conservative Laplace kernel method in one-step generative modeling.
citing papers explorer
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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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Identifiability and Stability of Generative Drifting with Companion-Elliptic Kernel Families
The paper proves identifiability of drifting fields for companion-elliptic kernels and shows that field convergence plus a C0 observable recovers weak convergence even without tightness.
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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.