Continuous-time consistency models are an attractive route to few-step generation. They remove the discretization error inherent to the timestep grid that discrete-time consistency models depend on. Until recently, however, training them was unstable. Lu & Song (2025) address this with the TrigFlow formulation and a coordinated set of architectural and training-objective changes. We conduct an independent empirical study of this framework on CIFAR-10 and ImageNet-64. No open-weight TrigFlow teachers exist at these scales, so we train them from scratch and then verify the consistency distillation (sCD) and consistency training (sCT) behavior of students initialized from these teachers. On CIFAR-10, our students reproduce the reported FID at one and two steps. On ImageNet-64, they fall short, a gap that appears related to our teacher and to architectural choices the paper leaves unspecified. We also report a parameter-count gap of about 5% between the model size stated in the paper and a faithful re-implementation, which we attribute to the scale-and-shift conditioning projections in Adaptive Double Normalization. We then propose Multistep sCD (MS-sCD), a continuous-time, segment-conditioned multistep generalization of sCD. The segment-conditioning idea is borrowed from the discrete-time multistep consistency distillation of Heek et al. (2024); we build on their preliminary continuous-time experiments within the TrigFlow/sCM framework. The rest of the algorithm follows sCD. MS-sCD replaces sCM's two-step intermediate time with a fixed segment-boundary schedule and recovers sCD at M = 1. We report FID at M = 2, 4, 8 and compare against the discrete-time MSCD baseline. Code, model weights, and training scripts are available on GitHub (Mathew et al., 2026).
Figures & tables
Dataset
Method
NFE
FID
ImageNet-64
EDM2-S ( Karras et al., 2024 )
63
1.58
ImageNet-64
TrigFlow teacher ( Lu and Song, 2025 )
63
1.70
ImageNet-64
TrigFlow teacher (ours)
63
1.83
CIFAR-10
TrigFlow teacher ( Lu and Song, 2025 )
35
2.15
CIFAR-10
TrigFlow teacher (ours)
35
2.08
Table 1: TrigFlow teacher FID, 50k samples, standard ADM evaluation. ImageNet-64 is class-conditional with the EDM2-S backbone. CIFAR-10 is unconditional with the DDPM++ backbone. The TrigFlow sampler is DPM-Solver-2S ( Lu et al., 2022 ) , with Heun’s intermediate step.
Method
Backbone
NFE=1 FID
NFE=2 FID
Framework
iCT-deep ( Song and Dhariwal, 2024 )
ADM-style
3.25
2.77
discrete, EDM
ECM-S * (ECT) ( Geng et al., 2025 )
EDM2-S
4.05
2.79
discrete, EDM
MSCD † ( Heek et al., 2024 )
UViT-small
4.3
2.0
discrete
sCM sCD-S ‡ ( Lu and Song, 2025 )
EDM2-S/TrigFlow
2.97
2.07
TrigFlow
sCM sCT-S ‡ ( Lu and Song, 2025 )
EDM2-S/TrigFlow
3.23
2.93
TrigFlow
Ours sCD
EDM2-S/TrigFlow
3.59
2.66
TrigFlow
Table 2: sCD and sCT results on ImageNet-64 (EDM2-S), without classifier-free guidance (CFG).
Method
NFE=1 FID
NFE=2 FID
Framework
iCT ( Song and Dhariwal, 2024 )
2.83
2.46
discrete, EDM
ECT ( Geng et al., 2025 )
3.60
2.11
discrete, EDM
CD-LPIPS ( Song et al., 2023 )
3.55
2.93
discrete, EDM
sCM sCD ( Lu and Song, 2025 )
3.66
2.52
TrigFlow
sCM sCT ( Lu and Song, 2025 )
2.85
2.06
TrigFlow
Ours sCD
3.59
2.39
TrigFlow
Table 3: sCD and sCT results on unconditional CIFAR-10, DDPM++ backbone, 50k samples. sCM paper numbers from Lu and Song (2025) , Table 1.
Figure 1: Green arrows are PF-ODE trajectories (data ↔ noise) and red arrows show the consistency map. (a) For M=1 the segment CM equation 14 reduces to sCM: fθ(0) collapses every trajectory point to the data origin (x0,0) . (b) For M>1 , MS-sCD splits the time axis at 0=t0<t1<⋯<tM=tmax and trains one segment-conditioned map fθ(k) per segment k . Each fθ(k) collapses trajectory points inside segment k to the segment’s lower boundary (xtk,tk) .
Method
M
NFE
FID
sCM sCD-S ( Lu and Song, 2025 ) (appendix Table 8)
1
1
2.97
sCM sCD-S ( Lu and Song, 2025 ) (appendix, 2-step)
1
2
2.07
MSCD on EDM2-S (ours)
2
2
3.44
MSCD on EDM2-S (ours)
4
4
2.32
MSCD on EDM2-S (ours)
8
8
1.79
MS-sCD (ours)
2
2
2.53
Table 4: MS-sCD vs. baselines on ImageNet-64 (EDM2-S, class-conditional, no CFG, 50k samples). sCM-S baselines are from Lu and Song (2025) , appendix Table 8, where the main-paper sCM table reports the XL variant for ImageNet-64. The MSCD baselines on the EDM2-S backbone are our reproductions of Heek et al. (2024) ’s method on this architecture.
Method
M
NFE
FID
MS-sCD (ours)
2
2
2.60
MS-sCD (ours)
4
4
2.35
MS-sCD (ours)
8
8
2.20
Ours sCT
1
2
2.09
TrigFlow teacher (ours)
—
35
2.08
TrigFlow teacher (ours)
—
199
2.22
Table 5: MS-sCD on unconditional CIFAR-10 (DDPM++ backbone, 50k samples). Teacher rows use DPM-Solver-2S on our TrigFlow teacher; the 35-NFE entry matches Table 1 . Two-step sCT is from Table 3 .
Figure 2: FID vs. NFE on ImageNet-64 (EDM2-S, class-conditional, no CFG, 50k samples). Solid lines: our EDM2-S/TrigFlow reproduction. Dashed lines: sCM’s reported sCD-S and sCT-S numbers ( Lu and Song, 2025 , appendix Table 8) . The two multistep students extend past the NFE≤2 regime of the single-step CMs by varying the number of segments M∈{2,4,8} : continuous MS-sCD (orange) leads at M=2 , while our discrete MSCD reproduction (purple) overtakes it by M=8 , both approaching the teacher reference (horizontal lines: ours 1.83 , sCM-reported 1.70 ).
Appendix figures & tables6 assets
Supplementary material from the paper’s appendix.
Appendix
Method
NFE
FID
sCD iterated
1
3.59
sCD iterated
2
2.66
sCD iterated
4
2.48
sCD iterated
8
2.32
MS-sCD
2
2.53
MS-sCD
4
2.26
Appendix
Table 6: Iterative single-step sCD vs. MS-sCD on ImageNet-64 (EDM2-S, class-conditional, no CFG, 50k samples). The sCD results at NFE =1 / 2 are from Table 2 ; MS-sCD results are from Table 4 .
Teacher
sCD
sCT
MS-sCD
MSCD-EDM
MM
Framework
TrigFlow
TrigFlow
TrigFlow
TrigFlow
EDM
EDM
Model
EDM2-S
EDM2-S
EDM2-S
EDM2-S
EDM2-S
EDM-S
Batch size
2048
2048
2048
2048
2048
2048
GPUs
32
32
32
32
32
16
Pmean
−0.8
−1.0
−1.0
−1.0
−0.8
—
Pstd
1.6
1.6
1.6
1.6
1.6
—
Appendix
Table 7: Hyperparameters for all experiments.
Model
NFE
Best
Mean ± std
TrigFlow teacher
63
1.83
1.8334±0.0005
sCD
1
3.59
3.6423±0.0330
sCD
2
2.66
2.6856±0.0153
sCT
1
4.34
4.4403±0.0557
sCT
2
3.98
4.0093±0.0198
MS-sCD ( M=2 )
2
2.53
2.5761±0.0231
Appendix
Table 8: ImageNet-64 seed FID mean ± std (EDM2-S, class-conditional, no CFG, 50k samples). Best matches the main-text FID.
Model
NFE
FID
P
R
D
C
TrigFlow teacher
63
1.83
0.802
0.708
1.165
0.968
sCD
1
3.59
0.776
0.703
1.062
0.950
sCD
2
2.66
0.780
0.708
1.104
0.960
sCT
1
4.34
0.722
0.737
0.878
0.900
sCT
2
3.98
0.719
0.747
0.890
0.904
MS-sCD ( M=2 )
2
2.53
0.785
0.702
1.121
0.960
Appendix
Table 9: ImageNet-64 precision (P), recall (R), density (D), and coverage (C) on the best-seed 50k-sample sets (EDM2-S, class-conditional, no CFG), using unnormalized 2048-d Inception-2015 features and k=5 ( Naeem et al., 2020 ) .
Consistency Models are generative models trained to map points along a diffusion trajectory to the same clean sample, enabling fast few-step generation.
Flow and diffusion models suffer from slow inference due to computationally expensive numerical integration. Distillation provides a promising way for a student model to learn from a teacher's dynamics, enabling one-step or few-step generation. However, existing methods often depend on curated distillation datasets, costly teacher rollouts, or auxiliary proxy networks, which complicate model training and scaling. In this work, we propose Consistent Distribution Matching, a simulation-free and data-free distillation method for accelerating diffusion and flow models while preserving strong generative capacity. Our key insight is to unify sample generation and score estimation with one student network. Thus, our framework uses only two models, a frozen teacher and a trainable student, and optimizes one objective. We prove that minimizing our objective indicates Wasserstein convergence of the student flow-map pushforwards to the teacher marginals. On ImageNet 256×256, our method attains an FID of 2.04 with a single function evaluation (1-NFE) and a 4-NFE FID of 1.37 within 40 epochs of training, surpassing the state-of-the-art distillation baselines without data. Our code code and model are available at https://consistentdmd.github.io/.
Yuxiang Fu, Qi Yan, Zike Wu +4
University of British Columbia · Vector Institute for AI · Canada CIFAR AI Chair
The slow iterative sampling nature remains a major bottleneck for the practical deployment of diffusion and flow-based generative models. While consistency models (CMs) represent a state-of-the-art distillation-based approach for efficient generation, their large-scale application is still limited by two key issues: training instability and inflexible sampling. Existing methods seek to mitigate these problems through architectural adjustments or regularized objectives, yet overlook the critical reliance on trajectory selection. In this work, we first conduct an analysis on these two limitations: training instability originates from loss divergence induced by unstable self-supervised term, whereas sampling inflexibility arises from error accumulation. Based on these insights and analysis, we propose the Dual-End Consistency Model (DE-CM) that selects vital sub-trajectory clusters to achieve stable and effective training. DE-CM decomposes the PF-ODE trajectory and selects three critical sub-trajectories as optimization targets. Specifically, our approach leverages continuous-time CMs objectives to achieve few-step distillation and utilizes flow matching as a boundary regularizer to stabilize the training process. Furthermore, we propose a novel noise-to-noisy (N2N) mapping that can map noise to any point, thereby alleviating the error accumulation in the first step. Extensive experimental results show the effectiveness of our method: it achieves a state-of-the-art FID score of 1.70 in one-step generation on the ImageNet 256x256 dataset, outperforming existing CM-based one-step approaches.
Linwei Dong, Ruoyu Guo, Ge Bai +3
1Zhejiang University · 2Bytedance Inc. · 3Zhejiang Lab
Step distillation has become a leading technique for accelerating diffusion models, among which Distribution Matching Distillation (DMD) and Consistency Distillation are two representative paradigms. While consistency methods enforce self-consistency along the full PF-ODE trajectory to steer it toward the clean data manifold, vanilla DMD relies on sparse supervision at a few predefined discrete timesteps. This restricted discrete-time formulation and mode-seeking nature of the reverse KL divergence tends to exhibit visual artifacts and over-smoothed outputs, often necessitating complex auxiliary modules -- such as GANs or reward models -- to restore visual fidelity. In this work, we introduce Continuous-Time Distribution Matching (CDM), migrating the DMD framework from discrete anchoring to continuous optimization for the first time. CDM achieves this through two continuous-time designs. First, we replace the fixed discrete schedule with a dynamic continuous schedule of random length, so that distribution matching is enforced at arbitrary points along sampling trajectories rather than only at a few fixed anchors. Second, we propose a continuous-time alignment objective that performs active off-trajectory matching on latents extrapolated via the student's velocity field, improving generalization and preserving fine visual details. Extensive experiments on different architectures, including SD3-Medium and Longcat-Image, demonstrate that CDM provides highly competitive visual fidelity for few-step image generation without relying on complex auxiliary objectives. Code is available at https://github.com/byliutao/cdm.
Tao Liu, Hao Yan, Mengting Chen +8
1VCIP, College of Computer Science, Nankai University · 2Alibaba Group · College of Artificial Intelligence, Jilin University