Generative Vision Atlas

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Generative Modeling via Drifting

Mingyang Deng, He Li, Tianhong Li, Yilun Du, Kaiming He · MIT · 2026-02 · arXiv:2602.04770

Why it matters

Learns a generator mapping directly, rather than a score or an instantaneous velocity to be integrated at sampling time. Training evolves the mapping's pushforward distribution along a drifting field until it matches the data distribution, an equilibrium condition. The result is natively one-step at inference — not a distilled multi-step model — and reports 1.54 one-step FID on ImageNet 256 in latent space, 1.61 in pixel space.

What this paper does

read: full text

Before this

Diffusion and flow matching both learn a local quantity — a score or an instantaneous velocity — and then integrate it over many network evaluations at sampling time.

The problem

That iteration is the cost. Getting to one step has meant distilling a trained multi-step model afterwards, inheriting the teacher's errors and paying for two training runs.

The idea

Move the iteration from inference into training. Learn the generator mapping directly, and let the training process itself evolve the distribution that mapping induces until it matches the data.

How it works

A drifting field V(x) is defined as an expectation over a kernel taking one real sample and one generated sample, decomposing into attraction toward data and repulsion from the model's own current output. Training is a fixed-point iteration: the generator is nudged along this field, implemented as a loss that regresses the generator toward its own drifted output under a stop-gradient. That stop-gradient is the key difference from flow matching, which regresses toward an externally specified target. Equilibrium is the condition V equals zero, which by anti-symmetry holds when the generated distribution equals the data distribution. Inference applies the generator once.

Evidence

1.54 FID in latent space and 1.61 in pixel space on ImageNet 256, at one function evaluation, trained from scratch rather than distilled.

Limitations

The authors state two clearly. The converse of their equilibrium result does not hold in theory: a near-zero drift does not formally guarantee the distributions match. And empirically they were unable to make the method work on ImageNet without a feature encoder, which they attribute to kernel design being unsuited to raw pixel space.

Why it matters

It is a genuinely different derivation from diffusion, flow matching and the average-velocity family, and it reaches one-step quality without a teacher. The admitted dependence on a feature encoder is also a data point for the representation argument: even a method built to avoid iterative sampling could not escape needing a learned representation to work.

Abstract, in the authors' own words

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.

Research line

Natively few-step objectivesemerging

Reported results

BenchmarkValueGuidanceBudgetSource
ImageNet 256x256 gFID (NFE=1)1.61not statednot statedabstract
ImageNet 256x256 gFID (NFE=1)1.54not statednot statedabstract

One-step, pixel space. Notable because it is within 0.07 FID of the same method's latent-space result, which is evidence against the latent being essential.

One-step (NFE=1). Not comparable to the multi-step rows above; the relevant comparison is against other one-step methods.

Design-axis choices

Objective

Drifting field

Method note — the shared flow-matching interpolation

Every flow-matching / rectified-flow paper in this atlas trains toward a straight-line path between a noise sample x₀ and a data sample x₁:

xt=(1−t) x0+t x1,vθ(xt,t)≈x1−x0x_t = (1-t)\,x_0 + t\,x_1, \qquad v_\theta(x_t, t) \approx x_1 - x_0

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