One-Step Diffusion Samplers

• One-step diffusion samplers are generative models that convert complex multi-step denoising trajectories into a single forward pass, enabling rapid sample generation.
• They leverage distillation techniques, such as Distribution Matching and Score Implicit Matching, to approximate the full denoising process with orders-of-magnitude acceleration.
• Advanced methods and shortcut flows ensure that these samplers achieve competitive metrics in vision, language, and audio tasks while supporting real-time applications.

A one-step diffusion sampler is a generative model that produces samples from complex target distributions in a single feed-forward pass by distilling or modifying traditional multi-step diffusion models. Standard diffusion models, which sequentially denoise Gaussian noise through dozens to thousands of network evaluations, generate state-of-the-art outputs in domains such as vision, language, and voice but are computationally intensive at inference. One-step samplers bypass this bottleneck by learning to approximate the full multi-step denoising trajectory in a single forward computation, achieving orders-of-magnitude acceleration while closely matching sample quality. The past two years have seen the emergence of principled frameworks—including Distribution Matching Distillation, Score Implicit Matching, EM Distillation, consistent shortcut methods, self-distilled ODE flows, and data-free divergence minimization—that transform pretrained or bespoke diffusion architectures into highly efficient one-step generators across modalities and tasks (Yin et al., 2023, Luo et al., 22 Oct 2024, Xie et al., 27 May 2024, Jutras-Dubé et al., 11 Feb 2025, Jutras-Dube et al., 4 Dec 2025, Kaneko et al., 3 Sep 2024, Zhu et al., 17 Jul 2024, Chen et al., 30 May 2025, Xu, 21 Aug 2025, Geng et al., 2023, Chen et al., 2023, Wang et al., 16 Jul 2025).

1. Formulation and Motivations

Classic diffusion samplers integrate a stochastic differential equation (SDE) or its deterministic probability-flow ODE, progressively mapping Gaussian noise $x_T \sim \mathcal{N}(0,I)$ at high noise levels down to a clean data point $x_0 \sim p_{\rm real}$ or another target density. Each step applies a score-based denoiser or control field, requiring $N \sim 20$–$1000$ expensive forward passes. In contrast, the one-step diffusion paradigm seeks a generator network $G_\theta(z)$, $z \sim \mathcal{N}(0,I)$, such that the output $x = G_\theta(z)$ is a direct sample from the target distribution, collapsing the multi-step denoising trajectory into a single, highly amortized mapping (Yin et al., 2023). This is achieved either by distilling the behavior of the full multi-step chain or by constructing architectures and training regimes that render multi-step refinement unnecessary.

The primary motivations are:

• Throughput: accelerating inference by $10^2$–$10^3 \times$ (e.g. 20 FPS on ImageNet 64×64 at FID ≤3) (Yin et al., 2023);
• Real-time and resource-constrained deployment: enabling interactive applications and scalable batch generation;
• Bidirectional contexts and sequence parallelism: as in continuous diffusion LLMs, where full-token parallelism removes autoregressive bottlenecks (Chen et al., 30 May 2025);
• Unified estimation for unnormalized targets: supporting tractable inference and evidence estimation in Bayesian applications (Jutras-Dube et al., 4 Dec 2025, Jutras-Dubé et al., 11 Feb 2025).

2. Distillation and Distribution Matching Techniques

A central strategy for training one-step samplers is distillation, wherein a student generator is optimized to match the output distribution of a pretrained teacher diffusion model. Distribution Matching Distillation (DMD) minimizes an approximate KL divergence between the student generator distribution $q_\theta(x)$ and the teacher output $p_{\rm real}(x)$, using the "score gradient identity" to reduce the parameter gradient to a difference of learned scores:

$$\nabla_\theta D_{KL} = \mathbb{E}_z \big[(s_{\rm fake}(x) - s_{\rm real}(x)) \nabla_\theta G_\theta(z)\big], \quad x = G_\theta(z)$$

where $s_{\rm real}$ and $s_{\rm fake}$ are score networks approximating gradients of the log-density under teacher and student distributions, respectively (Yin et al., 2023). DMD combines score matching with a regression loss on precomputed noise/sample pairs to ensure geometric fidelity, outperforming all published few-step methods: FID = 2.62 (ImageNet 64×64, 1 step), FID = 11.49 (MS-COCO30k, guidance 3), accelerating inference by $500\times$ with minimal perceptual degradation.

Score Implicit Matching (SIM) (Luo et al., 22 Oct 2024) provides a divergence-minimization formalism for one-step distillation, introducing an integrated score divergence over marginals,

$$\mathcal{D}^{[0,T]}(p_\theta, q) = \int_0^T w(t) \mathbb{E}_{x_t \sim \pi_t} [\mathbf{d}(s_{p_{\theta, t}}(x_t) - s_{q_t}(x_t))]$$

and demonstrates that, under regularity, the gradient with respect to $\theta$ can be computed efficiently even for implicit generators. SIM achieves FID = 2.06 on unconditional CIFAR-10 with no data-access required during distillation.

Other frameworks such as EM Distillation (EMD) (Xie et al., 27 May 2024) approach the problem as latent-variable maximum-likelihood inference, optimizing the forward KL and leveraging joint Langevin updates in the generator latent and noise variables, stabilized by a critical noise cancellation technique. This produces state-of-the-art FIDs (2.20 on ImageNet64 for EMD-16 with 1 step) and is robust to modal structure.

3. Self-Consistency and Shortcut Flows

One-step shortcut samplers have been constructed by enforcing consistency across step resolutions in the deterministic ODE associated with diffusion. Single-Step Consistent Diffusion Samplers (CDDS, SCDS) engage a consistency loss after integrating the probability-flow ODE from a given anchor $(x_t, t)$ through two possible routes: one large shortcut (student) and two intermediate steps (teacher), enforcing

$$L_{\rm state} = \mathbb{E}_{x_t, t, d} [\| \Psi_\theta(x_t; t, d) - \Psi_{\theta'}(\Psi_{\theta'}(x_t; t, d/2); t + d/2, d/2) \|^2 ]$$

where $\Psi$ denotes ODE integration (Jutras-Dube et al., 4 Dec 2025). Such self-distillation ensures that shortcut mappings reproduce trajectories of fine-grained multi-step samplers, and a volume-consistency regularizer aligns accumulated log-Jacobian changes for stable evidence (ELBO) estimation in unnormalized cases. In the generative setting, SCDS constructs step- and time-conditioned controls $u_\psi(x, t, d)$ and learns both sampling and shortcut dynamics from scratch (Jutras-Dubé et al., 11 Feb 2025).

Shortcut samplers "amortize exploration," delivering competitive Sinkhorn distances and log-partition function estimation on multimodal and high-dimensional density benchmarks with only 1–2 forward passes.

4. Advanced Frameworks and Model Compression

Architectural advances extend one-step paradigms to efficient large-scale and compact models. SlimFlow (Zhu et al., 17 Jul 2024) addresses the challenge of model compression, using the rectified flow framework to strengthen single-step samplers of minimal size (≈15.7M parameters). Annealing reflow adapts small students to the teacher flow via a beta-scaled hybrid mixing of random and teacher-generated pairs, and flow-guided distillation introduces a two-step regularizer that compensates for capacity limitations when matching intermediate flows offline and online. SlimFlow achieves FID = 5.02 at 15.7M parameters on CIFAR-10, outperforming all prior one-step samplers of similar scale.

In language modeling, DLM-One (Chen et al., 30 May 2025) generalizes score-distillation to continuous text generation. Student generators align their embedding scores with those of a pretrained teacher DLM, using alternating denoising score-matching and adversarial regularization. This collapses 2000-step DiffuSeq inference to one-step, speeding up generation by $>500\times$ on text generation benchmarks with only 5% drop in BLEU/ROUGE and similar empirical diversity.

Deep Equilibrium Models (DEQs) (Geng et al., 2023) present GET, a ViT-style transformer distilled offline using direct pixel-space regression on noise–image pairs from the teacher sampler. The core component is an implicit fixed-point transformer block solvable by Anderson acceleration, offering weight-tying regularization and adaptive test-time quality tradeoffs with $O(1)$ memory overhead.

5. Domain Extensions and Applications

One-step samplers have demonstrated broad applicability:

• Voice Conversion: FastVoiceGrad (Kaneko et al., 3 Sep 2024) distills a 30-step stochastic teacher into a one-step U-Net generator via adversarial conditional diffusion distillation (ACDD), blending GAN waveform adversarial loss and diffusion distillation. Empirical results reveal VC performance matching or exceeding multi-step baselines on VCTK and LibriTTS, with real-time generation.
• Autonomous Vehicles: Robust planners exploit single-step denoising diffusion samplers—distilled from a 1000-step teacher—capable of efficient failure-case sampling for collision prediction and risk-aware trajectory planning, achieving superior failure and delay rates compared to classical models (Wang et al., 16 Jul 2025).
• Acceleration in Pretrained Models: Skipped-step sampling exploits the Markov structure of DDPM, allowing a closed-form reverse skip from $T \rightarrow 0$ in standard architectures without retraining. Empirical results confirm substantial speed-ups with moderate quality loss, and hybrid approaches combine coarse skips with a few fine refinement steps for improved fidelity (Xu, 21 Aug 2025).

6. Theoretical Guarantees, Performance, and Limitations

Several frameworks provide non-asymptotic guarantees:

• Restoration–degradation analysis for deterministic DDIM-type samplers proves polynomial convergence bounds for the one-step ODE under mild Lipschitz and regularity conditions (KL/TV bounds with explicit dependence on step and restoration parameters) (Chen et al., 2023).
• Consistent shortcut distillation and deterministic-flow importance weighting yield unbiased evidence estimates and robust sample quality at extreme efficiency—often with $<1\%$ of the function evaluations used by traditional samplers (Jutras-Dubé et al., 11 Feb 2025, Jutras-Dube et al., 4 Dec 2025).

Leading one-step methods match or exceed previous few-step and GAN baselines in established metrics:

• Vision: SIM achieves FID = 2.06 (unconditional CIFAR-10, 1-step), 1.96 (class-conditional), and outperforms SDXL-TURBO and HYPER-SDXL in T2I aesthetic scores (Luo et al., 22 Oct 2024).
• Text: DLM-One yields BLEU within 1–5% of DiffuSeq with ~500× speedup (Chen et al., 30 May 2025).
• Sound: FastVoiceGrad matches 30-step VC performance at ≈30× lower compute (Kaneko et al., 3 Sep 2024).

Residual quality gaps (textural artifacts, lower coverage of rare modes) persist versus multi-step or large teacher models, especially at very high guidance. Limitations include the inherited failure modes of the teacher, challenges in tuning for diversity versus mode-seeking, quantization errors in token mapping, and, in high-dimensional or fine-detail settings, the need for further refinements or hybrid approaches. Robustness and calibration for likelihood estimation in heavy-duty Bayesian tasks requires geometric regularization, as provided by volume-consistency constraints.

7. Outlook and Future Directions

The field is converging toward highly efficient distillation, robust shortcut flows, and data-free divergence minimization for generative modeling:

• Theoretical analysis continues on optimal divergence choices (Fisher, pseudo-Huber, $\alpha$-norms) and on the stability of score matching via implicit generator gradients (Luo et al., 22 Oct 2024).
• Larger teacher models are expected to further close the quality gap with only marginal increases in distillation cost (Yin et al., 2023).
• Multimodal and cross-domain extensions, such as vision–language or video, are a natural fit for one-step score alignment and shortcut methods.
• Model size and memory footprint reduction will be addressed by flow rectification, annealing, and few-step regularizers (Zhu et al., 17 Jul 2024).
• The integration of deterministic Jacobian-weighted samplers provides a principled route to stable evidence estimation, expanding applicability in scientific and Bayesian domains (Jutras-Dube et al., 4 Dec 2025).

The rapid maturation of one-step diffusion techniques is redefining the efficiency–quality frontier for generative modeling, opening new pathways for deployment in real-time, large-scale, and data-sensitive environments.