One-Step Consistency Model

• One-step consistency models are generative frameworks that directly map a noisy state to data in a single network evaluation, bypassing iterative denoising.
• The approach employs a consistency function constant along an ODE trajectory, supporting one-step generation, multistep correction, and zero-shot editing tasks.
• Key advancements include direct-from-data training, adversarial consistency, and truncated-time optimization, enhancing speed and fidelity in image, speech, and remote-sensing tasks.

Searching arXiv for recent and foundational papers on one-step consistency models. A one-step consistency model is a generative model that learns a single mapping from a noisy state on a diffusion or probability-flow ODE trajectory directly to data, so that sampling requires one network evaluation rather than an iterative denoising chain. In the original formulation, a consistency function is constant along a trajectory of the probability-flow ODE and satisfies an identity boundary condition at the zero-noise endpoint; once trained, one draws a terminal Gaussian sample and applies the learned map once to obtain a generated sample. This formulation was introduced to retain the empirical strengths of diffusion modeling while removing its slow sampling bottleneck, and it supports both one-step generation and, when desired, multistep sampling and zero-shot data editing such as image inpainting, colorization, and super-resolution (Song et al., 2023).

1. Origins and defining idea

Diffusion models generate high-quality samples by repeatedly denoising, but their inference cost scales with the number of solver steps. Consistency models were introduced as a family of models that “generate high quality samples by directly mapping noise to data,” with one-step generation “by design” (Song et al., 2023). In the probability-flow ODE view, one considers trajectories $\{x_t\}_{t\in[\epsilon,T]}$ satisfying

$\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$

where $s_\theta(x,t)$ approximates $\nabla_x \log p_t(x)$. A consistency function $C$ is defined so that for every point on the same trajectory,

$C(x_t,t)=x_\epsilon,$

and hence $C(x_t,t)=C(x_{t'},t')$ whenever $x_t$ and $x_{t'}$ lie on that trajectory (Song et al., 2023).

The boundary condition is central: $C_\theta(x,\epsilon)\equiv x$. A standard parameterization enforces it through

$\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$0

with $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$1 and $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$2 (Song et al., 2023). After training, one-step sampling is the map

$\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$3

or, in variance-preserving notation, $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$4 followed by $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$5 (Song et al., 2023, Heek et al., 2024).

This establishes the basic distinction between one-step consistency and conventional diffusion. Diffusion learns a local denoising field and integrates it numerically; a one-step consistency model learns a global endpoint map. In the later “Multistep Consistency Models” formulation, this endpoint-regression view is embedded in a continuum: a $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$6-step consistency model is a conventional consistency model, whereas an $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$7-step consistency model is a diffusion model (Heek et al., 2024).

2. Mathematical formulation and training objectives

The common forward corruption model writes noisy data as

$\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$8

or, in DDPM notation,

$\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$9

The learning problem is then to recover $s_\theta(x,t)$0 from $s_\theta(x,t)$1 for any admissible $s_\theta(x,t)$2 (Song et al., 2023, Li et al., 2024).

The original distillation-based training objective constructs adjacent points on a discretized ODE trajectory. Given time points $s_\theta(x,t)$3 and a one-step numerical solver $s_\theta(x,t)$4, the distilled target $s_\theta(x,t)$5 is obtained from $s_\theta(x,t)$6 by one backward solver step, and the consistency-distillation loss is

$s_\theta(x,t)$7

where $s_\theta(x,t)$8 is an EMA target network and $s_\theta(x,t)$9 may be $\nabla_x \log p_t(x)$0, $\nabla_x \log p_t(x)$1, or LPIPS (Song et al., 2023).

A direct-from-data alternative dispenses with the diffusion teacher. “Improved Techniques for Training Consistency Models” formulates the one-step objective as

$\nabla_x \log p_t(x)$2

and interprets consistency training as directly matching student outputs at adjacent noise levels using the approximation $\nabla_x \log p_t(x)$3 for the reverse step (Song et al., 2023). In the $\nabla_x \log p_t(x)$4 limit, the paper states that consistency training is provably equivalent to distillation (Song et al., 2023).

The same pattern recurs across modalities. In speech enhancement, a consistency model $\nabla_x \log p_t(x)$5 is distilled from a diffusion teacher so that one ODE step

$\nabla_x \log p_t(x)$6

tracks the teacher’s multi-step ODE trajectory, and inference becomes

$\nabla_x \log p_t(x)$7

followed by iSTFT (Xu et al., 8 Jul 2025). In latent super-resolution, a single-step consistency model predicts a latent residual $\nabla_x \log p_t(x)$8 and a decoder reconstructs the final image (Sun et al., 25 Mar 2025).

3. Distillation, standalone training, and optimization refinements

Two training paradigms dominate the literature. The first is consistency distillation from a pretrained diffusion teacher; the second is standalone consistency training directly from data. The original paper explicitly supports both, but early best results relied heavily on distillation and learned metrics such as LPIPS (Song et al., 2023). Subsequent work concentrated on making direct training competitive.

“Improved Techniques for Training Consistency Models” identifies “a previously overlooked flaw” in consistency training with an EMA teacher. Its limit analysis shows that whenever $\nabla_x \log p_t(x)$9, the training objective “loses any dependence on the data”; accordingly, the paper sets $C$0 for the teacher used inside the training loss so that $C$1 at every step (Song et al., 2023). The same work replaces LPIPS with the Pseudo-Huber loss

$C$2

adopts a lognormal noise schedule, and doubles the total discretization steps during training. Combined with hyperparameter tuning, these changes yield one-step FID $C$3 on CIFAR-10 and $C$4 on ImageNet $C$5, with two-step FID $C$6 and $C$7, respectively (Song et al., 2023).

Another line of refinement argues that standard training spends excessive capacity on small-noise denoising rather than the ultimate noise-to-data mapping. “Truncated Consistency Models” restricts training to a truncated interval $C$8 and uses a two-stage procedure: standard pretraining on $C$9, followed by truncated-time fine-tuning while anchoring the model at the truncation boundary using a frozen pretrained consistency model (Lee et al., 2024). On CIFAR-10, the reported one-step and two-step FIDs are $C(x_t,t)=x_\epsilon,$0 and $C(x_t,t)=x_\epsilon,$1; on ImageNet $C(x_t,t)=x_\epsilon,$2, TCM with EDM2-S reports $C(x_t,t)=x_\epsilon,$3 and $C(x_t,t)=x_\epsilon,$4, and TCM with EDM2-XL reports $C(x_t,t)=x_\epsilon,$5 and $C(x_t,t)=x_\epsilon,$6 (Lee et al., 2024).

These results clarify a common misconception: one-step consistency models are not inherently tied to teacher distillation. Distillation remains common, but high-performing direct-from-data variants exist and, in some settings, surpass distillation-based baselines (Song et al., 2023, Lee et al., 2024).

4. Theoretical analyses and convergence guarantees

Theoretical work has focused on why self-consistency can approximate the endpoint of the reverse ODE and how training errors accumulate. “Towards a mathematical theory for consistency training in diffusion models” provides the first nonasymptotic $C(x_t,t)=x_\epsilon,$7 bound for consistency training (Li et al., 2024). Under a Lipschitz assumption on the true backward ODE maps and bounded-support assumptions on the data, it proves

$C(x_t,t)=x_\epsilon,$8

so that achieving $C(x_t,t)=x_\epsilon,$9 suffices with

$C(x_t,t)=C(x_{t'},t')$0

The paper presents this as a first theoretical justification for “single-call” sampling (Li et al., 2024).

A complementary analysis appears in “ACT-Diffusion.” There, the standard consistency loss is related directly to distributional discrepancy. With $C(x_t,t)=C(x_{t'},t')$1 assumed $C(x_t,t)=C(x_{t'},t')$2-Lipschitz in $C(x_t,t)=C(x_{t'},t')$3, the paper proves an upper bound

$C(x_t,t)=C(x_{t'},t')$4

where the accumulated term

$C(x_t,t)=C(x_{t'},t')$5

arises from recursive expansion across time steps (Kong et al., 2023). This theoretical picture explains why vanilla consistency training often requires very large batch sizes and large model capacity: later-time errors include earlier-time consistency deviations.

“Convergence Of Consistency Model With Multistep Sampling Under General Data Assumptions” weakens the data assumptions. For one-step sampling ($C(x_t,t)=C(x_{t'},t')$6), if the learned model satisfies approximate self-consistency and the data distribution has bounded support, it proves

$C(x_t,t)=C(x_{t'},t')$7

and also gives a total-variation result under an additional smoothness assumption after Gaussian smoothing (Chen et al., 6 May 2025).

Taken together, these analyses do not eliminate the known pessimism in high dimension; the $C(x_t,t)=C(x_{t'},t')$8 dependence and logarithmic factors are explicitly described as crude in current proofs (Li et al., 2024). They do, however, make precise that one-step consistency depends on both endpoint mismatch at large noise and accumulated self-consistency error along the training trajectory.

5. Adversarial, step-adaptive, and hybrid variants

One important extension replaces pure consistency losses with distributional matching at each time. “ACT-Diffusion: Efficient Adversarial Consistency Training for One-step Diffusion Models” introduces a discriminator $C(x_t,t)=C(x_{t'},t')$9 trained to distinguish real $x_t$0 from fake samples $x_t$1 (Kong et al., 2023). The generator and discriminator losses are

$x_t$2

and

$x_t$3

The usual GAN analysis then yields minimization of

$x_t$4

so the method directly drives the Jensen–Shannon divergence between the generated distribution and the true data toward zero (Kong et al., 2023).

Empirically, ACT reports one-step FID improvements on CIFAR-10, ImageNet $x_t$5, and LSUN Cat $x_t$6, while using “less than $x_t$7 of the original batch size and fewer than $x_t$8 of the model parameters and training steps compared to the baseline method” (Kong et al., 2023). On CIFAR-10, ACT-Aug reports FID $x_t$9 with batch size $x_{t'}$0, compared with CT at FID $x_{t'}$1 with batch size $x_{t'}$2 (Kong et al., 2023). The method also retains zero-shot image inpainting (Kong et al., 2023).

A second trend makes one-step models step-adaptive rather than strictly step-fixed. “Multistep Consistency Models” formalizes the interpolation between consistency and diffusion: $x_{t'}$3 is the conventional one-step model, and $x_{t'}$4 recovers diffusion (Heek et al., 2024). “SANA-Sprint” pushes this idea in text-to-image by using a continuous-time consistency model distilled from a pre-trained flow-matching model, augmented with latent adversarial distillation. The resulting student is “a unified step-adaptive model” for $x_{t'}$5–$x_{t'}$6 steps, with reported one-step performance of FID $x_{t'}$7 and GenEval $x_{t'}$8 (Chen et al., 12 Mar 2025).

A plausible implication is that the boundary between “one-step consistency model” and “few-step accelerated diffusion” is increasingly architectural rather than categorical: recent systems often preserve a one-step endpoint map while exposing an optional small-step refinement interface (Heek et al., 2024, Chen et al., 12 Mar 2025).

6. Cross-domain adaptations and empirical scope

One-step consistency models are no longer confined to unconditional image generation. The same endpoint-mapping principle has been adapted to speech synthesis, speech enhancement, super-resolution, portrait video generation, and related inverse problems.

Domain	Representative method	Reported one-step result
Image generation	"Consistency Models" (Song et al., 2023)	FID $x_{t'}$9 on CIFAR-10 and $C_\theta(x,\epsilon)\equiv x$0 on ImageNet $C_\theta(x,\epsilon)\equiv x$1
Direct consistency training	"Improved Techniques for Training Consistency Models" (Song et al., 2023)	FID $C_\theta(x,\epsilon)\equiv x$2 on CIFAR-10 and $C_\theta(x,\epsilon)\equiv x$3 on ImageNet $C_\theta(x,\epsilon)\equiv x$4
Speech synthesis	"CoMoSpeech" (Ye et al., 2023)	end-to-end RTF $C_\theta(x,\epsilon)\equiv x$5 (TTS) and $C_\theta(x,\epsilon)\equiv x$6 (SVS), i.e. $C_\theta(x,\epsilon)\equiv x$7 real-time
Speech enhancement	"ROSE-CD" (Xu et al., 8 Jul 2025)	$C_\theta(x,\epsilon)\equiv x$8 times faster inference speed; PESQ $C_\theta(x,\epsilon)\equiv x$9, SI-SDR $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$00 on VoiceBank-DEMAND
Remote-sensing SR	"Single-Step Latent Consistency Model for Remote Sensing Image Super-Resolution" (Sun et al., 25 Mar 2025)	$\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$01; PSNR $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$02, FID $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$03, LPIPS $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$04 on AID $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$05
Portrait video generation	"OSA-LCM" (Guo et al., 2024)	more than $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$06 faster; one-step FID $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$07, FVD $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$08

These adaptations preserve the central one-step mechanism while modifying conditioning, latent parameterization, and auxiliary losses. In CoMoSpeech, the consistency model is distilled from an EDM-style teacher over mel-spectrograms and uses one denoiser call to predict the mel before vocoding (Ye et al., 2023). In ROSE-CD, randomized learning trajectories and waveform-space PESQ and SI-SDR losses are added so that the distilled student can recover from teacher-induced errors and even surpass its $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$09-step teacher on in-domain and out-of-domain speech-enhancement benchmarks (Xu et al., 8 Jul 2025). In remote-sensing super-resolution, consistency learning is moved to a residual latent space to reduce cost and to concentrate modeling capacity on high-frequency detail (Sun et al., 25 Mar 2025). In portrait-video generation, OSA-LCM combines latent consistency with an avatar discriminator and a second-stage editing fine-tuning method to address the temporal gap in one-step generation (Guo et al., 2024).

7. Limitations, misconceptions, and open questions

Several limitations recur across the literature. First, one-step inference does not imply simple training. Vanilla consistency training has been reported to require very large batch sizes and large model capacity because error terms accumulate across time (Kong et al., 2023). Even when training succeeds, theoretical guarantees can be pessimistic in high dimension because current analyses scale as $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$10 up to logarithmic factors (Li et al., 2024).

Second, one-step does not mean teacher-free. Many high-performing systems remain explicitly teacher-student methods, including the original consistency-distillation setup, CoMoSpeech, ROSE-CD, OSA-LCM, and SANA-Sprint (Song et al., 2023, Ye et al., 2023, Xu et al., 8 Jul 2025, Guo et al., 2024, Chen et al., 12 Mar 2025). Conversely, improved direct training methods such as iCT, TCM, and CTMSR show that one-step consistency can also be learned from data without a pretrained diffusion model (Song et al., 2023, Lee et al., 2024, You et al., 26 Mar 2025).

Third, one-step does not preclude multistep use. The original formulation already “still allow[s] multistep sampling to trade compute for sample quality,” and subsequent work formalizes step-adaptive models that operate in one to a few steps (Song et al., 2023, Heek et al., 2024). This matters because the same model family is often evaluated both as a strict one-step generator and as a few-step corrector.

Finally, adversarial or auxiliary objectives introduce their own stability issues. ACT explicitly notes that tuning the $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$11 schedule and gradient penalties is crucial and that “too strong adversarial weight can cause mode collapse”; it also identifies stability on high-resolution $\frac{dx_t}{dt}=-t\,s_\theta(x_t,t),$12 and higher-dimensional inputs as requiring further study (Kong et al., 2023). More generally, the literature continues to explore other divergences, regularizers, truncated-time training schemes, randomized trajectories, and latent-space reformulations as ways to improve fidelity without forfeiting the central promise of one-step generation (Kong et al., 2023, Lee et al., 2024, Xu et al., 8 Jul 2025).

In aggregate, the one-step consistency model has evolved from a distillation mechanism for accelerating diffusion samplers into a broader framework for endpoint learning along diffusion or flow trajectories. Its defining property remains unchanged: a single network evaluation replaces iterative denoising. What has changed is the surrounding methodology—direct training, adversarial consistency, truncated-time optimization, step-adaptive sampling, and cross-modal specialization—which now determines whether a one-step model is merely fast or also competitive at the frontier of sample quality.