Weak-to-Strong Diffusion with Reflection
Authors: Lichen Bai
Masashi Sugiyama
Zeke Xie
Venue: ICLR 2026 Poster (2026)
Keywords: Diffusion Models
Diffusion Sampling
Text-to-Image Generation
Primary area: generative models
TL;DR: W2SD iteratively corrects the sampling trajectory by leveraging the gap between weak and strong models, significantly boosting the visual quality of images and videos with minimal extra cost.

Abstract: The goal of generative diffusion models is to align the learned distribution with the real data distribution through gradient score matching. However, inherent limitations of current generative models lead to an inevitable gap between generated data and real data. To address this, we propose Weak-to-Strong Diffusion (W2SD), a novel framework that utilizes the estimated gap between existing weak and strong models (i.e., weak-to-strong gap) to bridge the gap between an ideal model and a strong model. By employing a reflective operation that alternates between denoising and inversion with weak-to-strong gap, W2SD steers latent variables along sampling trajectories toward regions of the real data distribution. W2SD is highly flexible and broadly applicable, enabling diverse improvements through the strategic selection of weak-to-strong model pairs (e.g., DreamShaper vs. SD1.5, good experts vs. bad experts in MoE). Extensive experiments demonstrate that W2SD significantly improves human preference, aesthetic quality, and prompt adherence, achieving significantly improved performance across various modalities (e.g., image, video), architectures (e.g., UNet-based, DiT-based, MoE), and benchmarks. For example, Juggernaut-XL with W2SD can improve with the HPSv2 winning rate up to 90\% over the original results. Moreover, the performance gains achieved by W2SD markedly outweigh its additional computational overhead, while the cumulative improvements from different weak-to-strong gap further solidify its practical utility and deployability.

Published as a conference paper at ICLR 2026
WEAK-TO-STRONG DIFFUSION WITH REFLECTION
Lichen Bai
Masashi Sugiyama 2.3 Zeke Xie
"xLeaF Lab, The Hong Kong University of Science and Technology (Guangzhou)
"RIKEN AIP "The University of Tokyo
1bai292econnect.
zckexic@connect.
ABSTRACT
The goal of generative diffusion models is to align the learned distribution with the real data distribution through gradient score matching. However, inherent limitations of current generative models lead to inevitable gap between gen- erated data and real data. To address this, we propose Weak-to-Strong Diffusion (W2SD), novel framework that utilizes the estimated gap between existing weak and strong models (i.e., weak-to-strong gap) to bridge the gap between an ideal model and strong model. By employing a reflective operation that alternates between denoising and inversion with weak-to-strone gap, W2SD steers latent variables along sampling trajectories toward regions the real data distribution. W2SD is highly flexible and broadly applicable, enabling diverse improvements through the strategic selection of weak-to-strong model pairs (c.g.. DreamShaper SDI.5, good experts vs. bad experts in MoE). Extensive experiments demon- strate that W2SD significantly improves human preference, aesthetic quality, and prompt adherence, achieving significantly improved performance across various modalities (e.g., image, video), architectures (e.g., UNet-based DiT-based, MoE), and benchmarks. For example, JuggernattXLL with W2SD can improve with the HPSv2 winning rate to 90% over the original results. Moreover, the perfor- mance gains achieved by W2SD markedly outweigh its additional computational overhead, while the cumulative improvements from different weak-to-siie to-sonnn gap further solidify its practical utility and deployability.
INTRODUCTION
Standard Model
DEEP
ARN ING
W2SD (Ours)
Deep
Learning
Text:
Descriptions: tiger
Counting:
Color: pink green motorcyele.
Position:
Object cn-occurrence:
ssiign says 'Desp
two dogs sitiig on the gmass
photo sports right of an umbrella.
photo skateboard and cake.
Learning.
1980s Minmi vibe.
Figure 1: The qualitative results of standard Juggernaut-XX XL. and its W2SD version, where Juggernaut- XL acts strong model and SDXL. acts weak model. We present more cases in Appendix D.2
In probabilistic modeling, the estimated density represents model-predicted distributions while the ground truth density reflects actual data distributions. Diffusion models (Song et al.), known for its powerful generative capabilities and diversity, estimate the gradient the log probability densities in perturbed data distributions by optimizing score-based network. which has become mainstream paradigm in many generative tasks (Podell et al.] Guo et al. 2023 Shao et al. (025a) and discriminative tasks (Li et al. 2025)

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:M ()
M mnp (-)
Algorithm 1 W2SD
Xt-Ac
1: Input: Strong Model MM,, Weak Model M
Total Inference Steps: T, optimization steps:
À
x
2: Output: Clean Data
X
3: Sample Gaussian noise 27
A,(0)
4g(0) (4)
4:
for T to
5: if > T X then
6: #W2SD with Reflection
Figure 2: Visualizing the effectiveness of W2SD. When the weak-to-strone gap closely bridge the strong-to-ideal gap (e.g.. A2(t) - (t) is small), the refined latent variable F. converges to the ideal latent variable x.²
7: T. Min (MM, t),t)
end if
9: Tt-1 = ()),
10:
end for
Constrained by practical limitations including architectural design and dataset quality issues, existing diffusion models inevitably exhibit gradient estimation errors during inference stage, leading to modeling gap between the real data distribution and the learned one. This gap is always stubborn
defect of diffusion models, often causing various problems (Sadat et al. 2024 Liu et al. 2024b
Aithal et al. 2024 Huang et al., 20255).
A large body of work has focused on advanced sampling techniques through input conditioning (Zhou AAhn et al. 2024), architectural modifications (Si | 2024), and extra constraints (Chung al. 2022 He et al. 2023 Sabour al.) 2024) to bridge this gap between an existing model and an ideal one that can perfectly recover real data. For example, Z-Sampling Bai et al. 2024g improves sampling quality through implicit semantic injection, while
at 2024
(Karras et al., 2024)
requires training a degraded version of the model from scratch to guide the sampling process. Despite these efforts, improvements are often confined to isolated components and focus bridging the modeling gap from a single perspective (e.g., more ideal schedulers or denoising networks), leading to limited flexibility and generalization across different settings.
A natural question arises: can we flexibly leverage the various advantages of existing methods to further bridge the modeling gap and get closer to an ideal model(or real data distribution)? Our answer is affirmative. In this work, we propose Weak-to-Strong Diffusion (W2SD), a meta- improving framework that flexibly integrates some existing diffusion enhancement technique (as the strong model) and its corresponding weak version into the sampling process, enabling training-free free performance enhancement. To enable smoother and more effective gap bridging, departing from previous rough extrapolation methods (Karras et al. 2024). we draw upon a novel reflective operator into the diffusion sampling process in Figure 2 which is shown in Appendix E.5 be both more flexible and powerful. Instead of improving specific components, W2SD can generally leverage various weak-to-strong gaps to achieve a stronger model with a bridged strong-to-ideal gap. We also intuitively illustrate the motivation in Figure 4 The contributions can be summarized as follows.
First, we introduce a general weak tt-son concept into the inference enhancement diffusion models by flexibly leveraging various weak-to-strong gaps to bridge the modeling gap between strong model and the ideal mode, namely the real data distribution.
Second, we propose novel W2SD framework with reflection mechanism that alternately applies denoising with the strong model and inversion with the weak mode!"] which theoretically enables our framework implicitly estimate the weak-to-strong gap through iterative reflection, effectively steering latent variables along the sampling trajectory closer to the real data distribution.
Third, extensive experiments validate the effectiveness and broad applicability of W2SD across various generation tasks (c.g., image, video). architectures (c.g.. UNse-based, DiT-based), and evaluation metries. By extending the weak-to-strong concept, users can flexibly define weak-to-strong model pairs based on their specific needs. Depending on the type of model pair (e.g., DreamShaper vs. SDI.5; good experts vs. bad experts in MoE; ControlNet vs. DDIM), W2SD achieves diverse improvements in aspects such human preference, prompt adherence, and personalization. Notably, these improvements are cumulative and complementary. further enhancing generation quality. We provide a detailed application analysis in Section 4 Efficiency evaluations also show that W2SD's
In this work, we refer such inversion as diffusion reflection, following Bai al. 2024
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gains outweigh its computational overhead, maintaining superior quality under equal time constraints, which highlights its strong versatility and practical applicabilityy
2
PRELIMINARIES
In this section, we present preliminaries about denoising and inversion operation in diffusion mod- els (Song et al. Ho et al. 2020). Due page limitations, introduce more related works in Ap- pendix
Diffusion Model Given the random Gaussian noise 24, we denote the forward process of diffusion models as 22 At of Atz,, where [0. 1], and a represents the predefined variance. We denote the ground truth density of real data distribution as pū After noise addition time the resulting density represented as pf* Following DDIM (Song et al., 2020). we can obtain the denoised results 2t-Ar from noisy data 24. through the process of ordinary differential equation as
Tt-A: M(z,,
+ o²
o0 (x A), / [0, 1],
where se(.,-) represents the trained score network, utilized to predict the score at the time t. For simplicity, we set the noise schedule parameter (t) at. Similarly, here we can invert Equation [ to transform 2t-At back to a new ã;
34 = Mini (v+ (8t- Ar, 1),
(2)
= -t 0 0²1 so (It, t) At,
(3)
2
Ar, 0² (T) 1) E [0.
(4)
Given that the approximation error in Equation 44 is negligible and the same score netowrk se, M and Miny can be treated as mutually inverse mappings, thereby satisfying (M = Zt.
In Appendix E.3
we conduct detailed analysis of the impact caused by this approximation error.
Diffusion Sampling Enhancement As inference scaling laws (Wu et al. 2024) gain attention, increasing efforts (Bai al. 2024 Guo al. 2024 Ma et al. 2025) have been devoted to enhancing
diffusion models at inference time, Some recent techniques such as Z- Z-Smppligg (Bai et al. 2024) Auto-guidance and Auto- guidance (Karras al., 2024) can be approximately interpreted specific instances of
our framework with less flexibility and improvement. Z-Sampling (Bai et al. 2024) implicitly injects semantic information by exploiting the gap between guidance scales, which can be viewed as an instance of W2SD, we provide more analysis in Appendix E.4 Auto-Guidance (Karras et al.) 2024) relies on naive latent interpolation and training degraded version from scratch. In contrast, we propose that much broader range of strong-weak pairings can be leveraged in W2SD, not limited to slightly degraded models, but also including variations in input conditions and sampling strategies. Moreover, unlike Auto-Girtt Guidance that relies on CFG-like extrapolation and often introduces artifacts (Sadat et al. 2024), our smooth reflective mechanism effectively mitigates these issues (see Appendix E.5)
METHODOLOGY
In this section, we propose the Weak-to-Strow -ttrong Diffusion framework and interpret its mechanism.
3.1 WEAK-TO-STRONG DIFFUSION
In this subsection, we integrate the weak-to-strone concept into diffusion model inference, introduce the W2S framework, and establish its theoretical understanding.
The gap of Estimated Density Gradients In diffusiin models, the goal is to minimize the gradients gap log probability densities between estimated results and ground truth. However, due to the real data distribution is inaccessible. this gap cannot be directly quantified. To tackle this issue, consider models of varying capacities: a strong model (with its corresponding denoising process denoted as M and the estimated density pr) and weak model (similarly, " and p*).
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As shown in Figure 4 define the weak-to-strong gap A1 V llggp" V Vlogp" pM and the strong-to-ideal gap as Ag = V log V loggp". p". By approximating Ag using the estimable A1, we indirectly reduce the gap between existing diffusion models and the ideal model, bringing the learned distribution closer to the real data distribution. In the next subsection, we introduce how to achieve this approximation from reflective perspective.
W2SD Consider strong model M and a weak model M we can optimize the sampling trajectories using the reflection operator (MF(() as outlined in Algorithm [ Through the iterative integration of strong model denoising and weak model inversion, we achieve step-by-step reflective process during sampling process, refining the latent variable xy into an improved iy.
Importantly, the choice of MM and M significantly affects the direction of improvements effects. We summarize some promising weak-to-strong model pairs in Table of Appendix [C3 And in Section 4 we present extensive application analyses and experiments, highlighting the powerful capabilities and flexibility of the proposed framework.
In Theorem D we demonstrate that W2SD refines latent variable Tz toward the direction defined by the estimated weak-to-strong gap (t). As shown in Figure 2 when the weak-to-strong gap closely approximates the strong-to-ideal gap (i.e., A2(t)= - A (t) is small), the reflection mechanism of W2SD drives Fa closer to the ideal n²²². The visualization analysis in Section 3.2 validates the correctness of our theory, and we provide a detailed proof in Appendix [A.] In Appendix [.2] we present comprehensive qualitative and quantitative evidence suggesting that A effectively bridges (4). providing empirical validation for Theorem which also means that in Figure 2 the refined latent क, progressively approaches the ground truth latent Fgt--
Theorem (Theoretical Interpretation of W2SD) Suppose x; is the latent variable at time t, let pî and Dt denote the probability density estimates derived from M and M . The reflective operator M (-)) refines Ie to it as
i = It At( logpi(x;) Va, log (xt)),
(5)
where ( v. (x. V xe log (It) means the w2s gap between M and M at time t.
In Theorem 2 we also provide conditions for using A as a proxy for 22, with analytical validation. To further corroborate this, Figure 3 illustrates that given any two of the three models (weak, strong, or ideal), the third can be analytically derived to satisfy the theoretical constraints, providing visual verification of Theorem
Theorem (Error Bound for W2SD Approximation) Let the ideal, strong. and weak models (ó E {gt, s, w)) be infinite Gaussian Mixture Distributions p²() = f (H)N p. E)du. As- sume the normalized weight deviations of s and w relative to gt are characterized by polyno- mial bias functions B and B respectively. For any >> 0, if the relative bias ratio satisfies Ba x)) (% x) - S 6, then the error between the weak-to-strong gap A1(2) (x) and the strong- to-ideal gap A2(x) is bounded by:
(1(x)) -2 C (. (A2()),
(6)
where C(x) > 0 is a deviation efficiency function depending on distribution properties (see Ap- pendix A.2).
Furthermore, referencing Theorem 3 (detailed in Appendix A.3). we extend our analysis from local gaps global distribution alignment. We prove that under the relative bias condition of Theorem 2 (where error factor < 1), W2SD achieves strictly lower Fisher Divergence. The error reduction quantified as J J[ w2ad) S T ( < T[8 [|z²), confirming that the reflection operator
systematically reduces the total score matching error.
Finally, we analyze the limitations of W2SD when the bias consistency condition is violated. Two primary failure modes are identified: (1) Model Conflict FFiuure 22 where the weak and strong models exhibit opposing biases (i.e., bias ratio < 0), causing the W2S gap to contradict the true optimization direction; and (2) Model Over-similarity Figure 23 where the weak model mimics the strong model too closely (i.c., bias ratio xs 1 instead of 2). In this case, the resulting A is insufficient to bridge the gap the ground truth.
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10230)
I0500
IM350,
Figure 3: We modulate the weak model using Theorem 2 with the strong and ideal models fixed. A small allows the W2S gap to serve proxy for the S2I gap. For precise analysis, we derive the modulated weak model closed form via diffusion model based on GMM data distribution.
3.2 VISUALIZATION AND INTERPRETATION
In this subsection, we validate the theory presented in Section 3.1 using both synthetic Gaussian mixture data and real-world image data, providing intuitive visual evidence.
Diffusion trajectories via different samplinng strategies
Model
Swong Model
Dpenater
8-
7
timesteps
3
?
2
1
AT wask-lo-strong difereence
AZF strongg ideal diforencce
-2
Figure 4: W2SD aims to bridge the strong model toward the ideal model by using A proxy for 22. In the 1-D case, we expect W2SD can shift the sampling distribution towards the left mode at "-4", increasing the likelihood of gener- ating samples from low-density regions.
Predicted
Figure 5: W2SD balances the distribution by integrating a weak model (blue) and strong model (red) through reflection mechanism, re- sulting enhanced generation of samples in the left peak. We provide more cases in Figure 25
1-D Gaussian Mixture Data We begin by analyzing the 1-D Gaussian data scenario. In Figure the diffusion model is designed to generate data with distinct peaks at "-4" and "4". By adjusting the proportion of these two peaks in the training dataset, we obtain A and M In particular, Ms exhibits clear bias toward the right peak, often failing recover the left mode. In contrast, M demonstrates superior capability in capturing the structure of the left peak, indicating better generalization across modes. In Figure [5] we visualize the denoising trajectories under three different settings (weak model, strong model, W2SD). Through the reflective operator Mw (JM (-)), the latent variable is progressively drawn closer to the left peak. contrast, for both strong and weak models, the generated samples predominantly concentrated around the right peak.
2-D Gaussian Mixture Data 6 (first row), modulate the proportion of the training data to obtain M and M W2SD balances the distribution by exploiting the discrepancy between M and M (the region in the bottom-left corner, denoted A₁) bridge the unattainable strong-to-ideal gap A2, and boost
We also visualize the mechanism of W2SD on 2D scenario. In Fig-
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Soor
M
M
S2ND
W2SD
(Ours)
Figure 7: Qualitative results of W2SD based dataset gap (CIFAR-10). Our framework en- hances the probability of generating "cars" and promote more balanced generation distribution.
Figure 6: Prohability contour plot and denoising
trajectories across different settings (2-D Gauss).
the chances of sampling toward the bottom-left region. Figure (second (second row), we visualize the denoising trajectories under different settings. W2SD balances the learned distribution, bringing closer to the real data distribution. further validating the effectiveness of W2SD.
Real Image Data Furthermore, we investigate the performance of W2SD CIFAR-10 10 Krizhevsky iet al., 2009). For ease of analysis, we select two classes from CIFAR-I0 Krizhevsky et al. 2009): car and horse. Specifically, the weak and strong diffusion models are trained on distinct datasets. Both MM' and MM are biased toward generating horses. Moreover, since A is trained on only a limited number of car images, it rarely generates cars. In Figure 7 W2SD can help balance the image categories, enhancing inference process to increase the probability of generating cars. In Figure 18 also perform t-SNE dimensionality reduction (Van der Maaten & Hinton 2008) on the CLIIP features of the generated images. W2SD effectively disentangles the representations of "car" and "horse" in the 2D space. We proivde more details in Appendix E.2
4 EMPIRICAL ANALYSIS
In this section, we justify our design choices in Section and illustrate the wide applicability and impressive improvement of W2SD across diverse weak-to-strong combinations of M and M Due to page limitations, we present more quantitative and qualitative results across diverse benchmarks (e.g., Drawbench (Saharia et al. 2022)) and modalities (e.g., video generation) in Appendix D
Experimental Setting We present experimental results across three diverse model gap settings. For clarity, summary of these veta-experimental results is provided in Table For reliable evaluation, metrics: HPS v2 and PickScore for human preference alignment; AES for aesthetic quality; CLIP-T and CLIP-I for personalized generation in LoRA models; and FID & Inception Score (IS) for MoE expert selection strategies, measured against the training data distribution. We present more experimental details Appendix C
we use configuration-specin
Table 1: Different types of model gap lead to improvement effects in different directions.
Model Gap
M
M
Results
Finetune Mechanism
SDXL/SD1.5 SDXL/SD1.5 Weak experts (MoB)
Tables
and
Weight Gap
LoRA Mechanism
Tables 10
and
Strong Experts (MoE)
Table
High CFG
Low CFG
Tables 5 and
Condition Gap
Refined Prompt
Raw Prompt
Table 6
ControlNet
Standard Pipeline (DDIM)
Figure 11
Sampling Pipeline Gap
IP-Adapter
Standard Pipeline (DDIM)
Figure
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Clothing
Character
Style
A dog in a balman costume..
Detail
Bulma is biking, pink dress, blue hair.
sandwich styled in the manner of parchment scroll.
mechanical bee flying in electronies, motors,
Figure 8: Qualitative comparisons with weak model (left), strong model (middle) and W2SD based on weight gap (right). Our framework utilizes the gaps between chosen strong and weak models (e.g.. high-detiil LoRA vs. standard model) deliver improvements various dimensions, including style, character, clothing, and beyond. We provide more qualitative results in Appendix D)2
4.1 WEIGHT GAP
The capability gap between models can be directly captured by their parameter weights. And W2SD leverages this weight gap to empirically bridge the strong-to-idest gap, enabling effective reflective operations.
Table 2: Quantitative results of W2SD based on full parameter fine-tuning strategy. Our framework generates results better aligned with human preferences. Datasets: Pick-a-Pic.
Table 3: Quantitative results W2SD based on personalized LoRA model. Here, We SD1.5 as weak model M and (SD1.5 + LoRA) as strong model M We note different LoRA modules enable distinct personalized outcomes, as shown Figure g and Appendix D.2
Method
HPS
PickScore
SD1.5
24.9558
5,5003
20.1368
DreamShhper
Method
DINO 1
CLIP-I
CLIP-T
WISD
30.4924
6.2478
21.5727
53.1304
SD1.5
27.47
$2.08
20.14
SDXI.
29,8701
6.09.39
21.6487
Personalized LoRA
48.03
64.37
25.99
Juggeraut-XL W2SD
31,6112
5.9790
22.1903
45.7397
W2SD
51.58
68.04
27.66
32.0992
6.0712
22.2434
54.2634
Full Parameter Fine-tuning We first select the full parameter fine-tuned models (e.g.. DreamShaper, Juggernaut-XD0 that align more closely with human preferences as AM,, and the corresponding standard models as M (c.g.. SD1.5 (Rombach al. 2022). SDXL (Podell et al.)). We evaluate our framework with various metrics, as shown in Table 2 W2SD based on weight gap shows significant improvements in human preference metrics such as HPS (Wu et al. 2023b) and
PickScore (Kirstain et al. 2023). We provide more visual cases in Figure 15 of Appendix D.2
LoRA Mechanism Furthermore, W2SD is also applicable efficiently fine-tuned model. select the personalized models derived through the LoRA mechanism (Hu et al.) as _MS, and employ W2SD attain more robust and customized personalization effect. We test 20 LoRA checkpoints across object, person, animal, and style categories, with details in Appendix
Table[3 demonstrates that W2SD results in significant improvements across multiple personalization metrics (e.g.. Clip- T and Cli We present the qualitative results in Figure with more visual cases in Appendix D.2
C.3
MoE Mechanism We also note that weak-to-strong gap be induced by controlling the expert selection strategy within the MoE mechanism. Specifically, we focus on DiT-MoE (Fei et al. 22024). novel architecture that integrates multiple experts and selects the two pethhsstperforming experts
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during each denoising step to optimize generation quality. Based on this framework, use DiT- MoE-S as MM and define M as the two lowest pereesr-proomingggg experts in each denoising step, thereby establishing quantifiable weight gap.
In Table we show that W2SD reduces FiD (Seitzer 2020) from 15.1032 to 9.1001, aligning the learned distribution closer to the real data distribution. Additionally, although the limited capacity of MoE-DiT-S (with only 71M active parameters) often results image degradation (the first row in Figure 9). the application of W2SD signifieantly enhances the image quality (the second row in Figure
Table 4: Quantitative Results of W2SD Based on MoE Mechanism. Dataset: ImageNet 50K.
Method
1S
FiD 4
AES f
HPS v2
DiT-MofE-S
45 45.4437
15.1032
4.4755
20,0486
W2SD
55.5341
9.1001
4.5053
22.3225
Table 5: Quantitative Results of W2SD Based on Guidance Gap. Dataset: Pick-a-Pic.
Figure 9: Quantitative Results of W2SD Based on the MoF. Mechanism. The first row shows the results for DiT-MoE-S, while the second row presents the results of W2SD. We note W2SD achieves significant improvements, even with small models featuring 71M activated parame- ters, effectively eliminating image distortion.
Method
HPS v2 f
AES
PickScore
MPS f
SD1.5 W2SD
24,9558
5.5003
20.1368
42.1101
25,5069
5,5073
20.2443
57,8903
SDXI
29.8701
6.0939
21.6487
43.9425
W2SD
31,2020
6.0970
21.7980
56.0608
4.2 CONDITION GAP
Here demonstrate that the weak-to-strong gap applies not only across different weights but also within the same diffusion model under the weak-to-strong conditions.
The classifier-free guidance mechanism (Ho & Salimans 2021 extrapolates between conditional and unconditional noise predictions, adjusting the guidance scale control the semantic attributes of the generated images. To apply W2SD, diffusion models under high guidance scale can be viewed as M those under low even negative guidance scale can be treated as M" This guidance scale discrepancy constructs weak-to-strowe distribution more closely with the semantic conditions of the prompt. In Table [5] our framework significantly enhances human preference (c.g., HPS v2) and aesthetic characteristics (e.g., AES) in mainstream models such as SDXL and SD1.5.
Guidance Scale
gap that aligns the learned generated
Table 7: The improvements effects from differ- ent model gaps can be cumulative. Datasets: Pick-a-Pic.
Table 6: Quantitative results of W2SD based on semantic gaps between prompts. Model: SDXL. Datasets: GenEval.
Weight Gup
Condition Gap
HPS y2
Winning Rate
Prompt Type
HIPS v2 f
PickScore
Raw Prompt
25.3897
5.4454
20.7144
x
31.6412
Refined Prompt
28.5698
21.6350
45.7719
32.8217
84%
W2SD
29.4023
5,8812
21,8053
54.2275
x
32.0992
76%
32.9623
90%
Semantics of Prompts Aside from adjusting the guidance scale, we demonstrate that the semantic gaps within the condition prompts themselves can also be leveraged to enhance generation qual- ity through the reflection process. Specifically, we select a total of 533 text prompts from the GenEval (Ghosh et al.) 2024) for M with an average length ranging from 5 to words and minimal contextual complexity. Additionally, we leverage LLM (here we use Qwen-Plus (Yang et al.) 2024) to enrich and refine these prompts with additional details for Mg. resulting in weak-to-strong prompt pairs. We report the quantitative results in Table 6 which relies solely on the semantic gaps between prompts, achieves improvements across all metrics. And in Figure of of Appendix D.2 show that W2SD is capable of more precisely capturing the details based the gaps in prompt pairs.
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4.3 SAMPLING PIPELINE GAP
Extensive works (Si et al. 2024 Chefer et al., 2023; Zhang et al. 2023) have been devoted to design advanced inference pipelines to improve the quality of diftusion generation results. We demonstrate that W2SD enhance the inference process by leveraging the gap derived from these powerful existing pipelines. Here we define those enhanced sampling methods as M while M represents the standard sampling (Song et al.
2020 Lu al. 2022).
We first select ControlNet (Zhang et al. 2023) as M which incorporates additional network structures into the pipeline. By utilizing reference images (e.g.. edge maps), facilitates controllable image generation. As shown in Figure 11 the images generated by W2Sd exhibit stronger alignment with the provided edge maps. We also present visualization results of strong models such IP- Adapter( Ye et al. 2023). as shown in Figure I0, with DDIM serving as the weak model. It can be observed that W2SD better aligns the generated results with the reference image. Therefore, our framework is largely orthogonal to efforts in the research community aimed at improving diffusion sampling. which significantly enhances the broad applicability of W2SD and further generalizes the weak-to-strong concept beyond (Karras et al. 2024).
Reforowse Tmmogs
Referewe Twage
IP-Adapter
W2SD(Ours)
IP-Adapter
W2SD(Ours)
A moon the sea.
A oldd man.
Figure 10: Qualative Results of W2SD based on pipeline gap. We set IP-Adapter M DDIM as
M.. W2SD makes the output better aligned with the reference image
Edge Map
ControlNet
W2SD (Ours)
Edge Map
ControlNet
W2SD (Ouns)
A little blue sprite is laughing.
Two purple oranges.
Results of W2SD based on pipeline gap. We set ControlNet as M DDIM as M". W2SD makes the output better aligned with the edge map.
Figure 11:
4.4 CUMULATIVE EFFECTS OF DIFFERENT MODEL GAPS
Finally, we note that the improvements effects of W2SD, derived from different type of gaps, can be even cumulative. Here we apply the weight gap and the condition gap simultaneously. where M represents the fine-tuned model Juggernaut-Xi with high guidance scale at 5.5, while M represents the standard model SDXL with low guidance scale at zero. As shown in Table 7 the combination of weight gap and condition gap leads to substantial improvement in Pick-a-Pic compared to M achieving a winning rate of up to 90% on HPS v2.
DISCUSSION AND ANALYSIS
In this section, we discuss and perform more detailed studies on W2SD.

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The Magnitude of Weak-to-Strong Gap In this subsection, explore how the magnitude of weak-to-strong gap affects the improvements effects. To quamtify the gap between M and MM, we first consider the LoRA-based W2SD framework. We fix the LoRA scale of M at 0.8 and adjust the LoRA scale of M (e.g., from -3.5 to 3.5) to observe its impact on the effects of improvements. As shown in Figure [2 (left), when the LoRA scale of M exceeds that of M", W2SD improves performance. However, when M is weaker than MM (i.e., the scale gap is negative), the improvements effects result in the negative gains.
In addition, as shown in Figure 12 (right), we also quantify the weak-to-strong gap based on guidance scale. By fixing the guidance scale of M at 5.5 and adjusting that of M (e.g., from -10 15), we observe similar phenomena. In Figure 13 we present qualitative analysis showing that the magnitude of the teak-to-strong gap is key factor to influence the generation quality.
MCOD
Bax evdel
LeBAD VeBAD-Rrraee
23.5
30
23.0
28-
32.5
32.0
24
31.5
22
Wo50
31.0
The diffrennee Lo
difference Guidance Scale
The magnitude weak-to-strong gap key factor impacting the effects of improve- ments The horizontal axis shows the magnitude of the weak-to-strong gap, while the vertical axis shows the average HPS v2 on the fick-a-Pic. When M weaker than M", W2SD results in negative gains.
Figure 12:
Figure 13:
When the weak-to-strong gap is greater than O, W2SD yields positive gains. When it equals 0 the process degenerates into standard sampling. When it is less than 0, nega- tive gains occurs, resulting in poor image quality.
Time Efficiency Comparison Assuming standard sampling and W2SD require Tstd and Tw2s denoising steps, respec- tively, the score predictions needed are Tstd and Tw2 2A. To ensure a fair sampling time efficiency comparison, we set Tw2 = T and X 1 matching the runtime for generating the same image. For example, Teta = 50, stan- dard sampling performs 50 denoising steps (e.g., DDIM), while W2SD uses Tw2s + 2 = 24 + 2 12 = 48, indicating that the time required generate single image is approximately equal. In this setting, as shown in Figure [4] W2SD consistently out- performs standard sampling, demonstrating that the gains from reflection operations far outweigh the additional computational cost, validating the time efficiency of our framework.
12.5
81.
11.3
33.5
30.0
29.5
25.
Standars Samsiiing
W2250
per Image
Figure 14: W2SD can outperform standard sampling by large mar- gin even under the same inference time with various inference steps.
For a more comparable analysis, we also examine the performance of W2SD under different settings of T and A, as shown in [9] and 20 The results demonstrate that performance consistently improves with increasing X for W2SD, time inference scaling method, across both turbo and classical models.
6 CONCLUSION
In this work, we systematically integrate the weak-to-stee mechanism into the inference enhance- ment of diffusion models. We theoretically and empirically indicate that the estimated weak-to-strong gap can effectively bridge the strong-to-iden gap, enhancing the alignment between the learned distributions from existing diffusion models and the real data distribution. Building on this concept, we propose W2SD, which utilizes the estimated gap in density gradients to optimize sampling trajec- tories via reflective operations. W2SD demonstrates its effectiveness as a purrpoe- framework through its cumulative performance improvements, flexible definition of weak-to-strone model pairs, and significant performance gains with minimal computational overhead. We believe that our work model pairs will motivate interesting works for more tasks in future.
that leverages
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ETHICS STATEMENT
This work introduces W2SD, a novel framework designed to enhance the inference process of diffusion models. The data and models utilized in our work are released under open-source licenses and sourced from open platforms. While our work may have various societal implications, it does not introduce additional ethnic concerns compared to existing standard sampling methods. As such, none which we feel must be specifically highlighted here.
ACKNOWLEDGEMENT
This work was supported by the National Natural Science Foundation of China under Grant No. 62506317 and Dream Set Off Kunpeng and Ascend Seed Program. MS was supported by JST ASPIRE Grant Number JPMJAP2405.
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A PROOFS
In this section, we provide the proofs for Theorem ] presented in this work.
A.1 PROOF OF THEOREM
We first establish the relationship between the latent variable x, and the refined latent variable öt through the reflection operation, proving that the core mechanism of W2SD is to optimize in the direction of the weak-to-strong gap.
Proof At given time the W2SD reflection operation applies the operator M M.) to the latent variable Tt.
Specifically, we first denoise 24 using the strong model M according to Equation At as
obtaining
It- + 0²² (g)
where sy denotes the score predicted by M which is equivalent to the gradient of the log probability density log so, Equation 7 can be rewritten
Tt = 34 Vx, log (x.)A..
(8)
After obtaining Tt- apply the weak model M to invert Tt- back to the noise level at time t according Equation thereby completing the reflection process as
3y 2 -1- - 0²'
- ( (14--0 1)At,
where Sy denotes the score predicted by M". Since At is typically small, we neglect the approxi- mation error in the diffusion inversion process which implies that $ø (Iı-Ai, t) is equivalent to the reformulate Equation (
gradient of the log probability density log P" Hence
Ι Zt-At " log P At.
(10)
Combining Equation and Equation
10
obtain āg
it It-A:
logp (zt)
(11)
= -t. V., log (x. Al o V,, logri (x))
(12)
= Iz + -o " de logp v., lo (zt)).
(13)
weak-tn- strong gap (1)
From Equation 13
we observe that for the latent variable It, the reflection operator MW (M)())
in W2SD perturbs x, along the direction of (t) producing the refined variable Zt. When the weak-to-streee strong gap A closely bridges the unattainable strong-to-ied prong-to-ideal gap Az(t), the resulting St becomes more aligned with the ground truth ideal distribution.
A.2 PROOF OF THEOREM 2
We now establish the theoretical connection between the weak-to-strong gap A and the strong-to- ideal gap Ag. providing the strict condition for W2SD to work effectively. It is worth noting that for A1 (t, z) and (z(t, x) at time step t with input æ, we simplify the notation to A (x) and Ag(z) for convenience, with the understanding that the analysis is conducted at step by default.
Proof 2 Consider three distributions represented by infinite Gaussian mixture models:
/ " w (1)N p1 E)dn,
(x)
p²(x) I (w' E)dp,
(14)
("(W)(EE Eldp, (x)
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where all models share the same covariance matrix Σ. representing common level of distribution concentration. Since infinite GMMs can theoretically approximate any continuous distribution, this assumption is well-founded and provides universal approximation capability for our theoretical framework.
Define the posterior weight function:
(ulo) w(p))
(15)
p(x)
and Equation (5) represents the probability that a given data point x was generated from the Gaussian component centered at μ. conditioned on the current observation.
The score function can then be expressed as
x V logp(z) = - x [
(16)
which reveals an intuitive geometric interpretation: the score function peintss from the current position toward the posterior mean [[ with the covariance matrix Σ controlling the strength and direction of this attraction.
The ideal gap and computable gap are respectively
(2(1) =- / (1)(())))))) - du
(17)
=- /
(
w w'(H)
W (2; M, 2) du,
po)(s)
p²(x))
A1(x) = -- (1b7((1a))) 7xhh (4|=x) dj
(18)
--Σ-1 I ( (m()) (x)
w0
(H)
) (x: 14 Σ) du
Specifically, to facilitate the analysis, we define
w (1)
w w
K
1
Σ
B (1,
(x))
p&l (x)
kmm
(19)
w (H)
wis (H)((H)
K
1
Bk m
(1, x.)
(x))
(x)
k=
where Bh and By represent the k-th order polynomial coefficients for the strong and weak models relative to the ideal model, respectively, and K. is the total polynomial order.
Building upon Equation 17 and Equation
19
we reformulate (z) as:
A2(2) --1 f
w (H)
wh (H)
Nax E)dμ
(x)
(x))
-- f
(
wH(HH)
(1+
(+
Σ By B+ (u))
K
)
NV N(t 21,)
(x)
(x)
(20)
par (x) / 1 (1))
E-1
By (1,x))
Ar(x: E)d
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Similarly. D1 (x) can be expressed as:
w (p)
(4)
(1 -ー
Na ps E)d
(x)
p²)x)
= =- /
(P(())
K
" (x)
++> B B (4. (
(1+
K
] Me Myddu E)d
1+
By (u)
(x)
(2)(())
(x) /
Σ-1
K
1wwF (w)
(1, - By (1)
N Nax;; u, E)du
Σ-1
I prof (p)
B (1,, x²) By (H, x)
-1 By B)(U.))) N(x;H, E)dp
(x)
(21)
Therefore, according Equation 20) and Equation should be as small as possible. And the condition A c Re (2 requires:
21
want (1(x) Re A2(x), i.. |A, A2ll
B (14, x)
1
(22)
B (H,
For any E >> O, under condition
B (1, x))
2 Se for all k I,.... K,
(23)
Bh
we can compute the difference
| 22(x)) as
|2-111
/ (mo (1)
B (p, x)
| (x) A2(+)) S (x))
-2
B¹ (u; N(a; u 2)du
(14
| '1 / 11al (4)
B (1,,ar)
2
B¹ Bh x))
N( 2dd4
(x))
By (1,,
R=1
S ||--1| / (1 (m))
B (1.22))
N(z; E)dn.
(x)
(24)
Substituting yields
[1))))) A2(x))l s. |
(x) / @ (w)
K
Σ
B¹ (u,
N( E)du.
(25)
Let:
11 (m)
Ex= K
(H, x3) N(x: n, E)du
C(x) = [ (w)
(26)
Ex= Bb(,x)) N E)dp
Then:
| A2(x))l se. 12-21
(x) / (1Al) (H)
K
Σ
B (4,20))) N u. E)dμ E)dH
= |
// (W)
( D N(a5, 2)d0
(27)
C(x) Se. ||A2(x)].
(x)
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The constant C(x) serves as a critical efficiency ratio that quantifies the relationship between the cumulative magnitude of model deviations and their net directional effect the score function. Mathematically, it represents the worst-case amplification factor between the absolute sum of strong model biases | (J) across all Gaussian components and the resultant vector norm of their integrated effect. A value of C(x) = indicates coherent directional biases that efficiently translate into score modifications, whereas ((x) >> signifies significant cancellation effects where substantial individual deviations yield minimal net impact on A2(r). This ratio fundamentally determines the tightness of the error bound and characterizes the spatial effectiveness of the generalization across the data manifold.
A.3 GLOBAL ERROR REDUCTION VIA FISHER DIVERGENCE
Under the conditions of Theorems I and 2, in this section, we demonstrate the theoretical advantage of W2SD over the standalone Strong Model.
While deriving tight global error bound for the entire sampling trajectory of generative diffusion models remains a challenging open problem the field, we can rigorously demonstrate that W2SD achieves lower local score estimation error compared to the strong model under the conditions derived in Theorem? 2 Since the global sampling error is the accumulation of local discretization errors, reducing the local error directly contributes to a lower total error. We formalize this claim 3 with the accompanying proof provided in Proof 3
in Theorem
Theorem (Global Error Reduction via Fisher Divergence) Let (**()) (x) denote the ground truth data distribution. Let I (y²*(1p²)) = 2 EEpespa VI log (x) - V log (x:))(] be the Fisher Divergence measuring the total score matching error.
Consider the refined score estimate of W2SD defined as (x) = V lz) ( (z)z). Under the approximation condition established in Theorem bounded by a factor E [0, 1) such that [| 22 S <2]A2(2)]], the total error of W2SD is strictly bounded by the total error of the strong model:
2 where the point-wise estimation error is
I J1p811p
I &T < ((ptt
(28)
This implies that W2SD theoretically achieves a globully superior generation quality compared to the standalone strong model.
The Fisher Divergence for the strong model M is given by the expectation of the squared norm of the strong-to-idedt to-ideal gap (2(z):
Proof 3
I (1*111p7) 1 f (x)] log - Vz (og
1 1/2 ʃ / (c)) (29)
For the W2SD framework, the refined score sw2ed(x) = V (x) The corresponding Fisher Divergence is:
J (p w2dd
vst (x) log - sw2nd ( 2xx
(3s(x)| log (x:) - (V, log Az)
(30)
(>)( loggs'((>> (z) V, logp(()))) (x)
/ (=))111222) (1)2)
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Based on the premise derived from Theorem 2 (relative bias consistency), we have the point-wise bound ||)(a)) (1(z) & e|(2(())1-- Substituting this inequality into the integral:
1 I J( 1122d1)022d) - (² (cl A2(x))l) dr
= = (2) p (t))l
(31)
= (10")11)>))
Since 0 S c < 1 holds for well- weak-to-stne to-soon pairs (as discussed in Theorem 2), it follows that I (p8t (ld)) < I (188"1pp²)
B RELATED WORK
In this section, we review existing works relevant to W2SD.
Weak-to-Strong Mechanism The concept of improving weak models into strong models origi- nates from the AdaBoost (Høgsgaard et al. 2023). which constructs a more accurate classifier by aggregating multiple weak classifiers. Building upon this, recent theoretical advances (Green Larsen & Ritzert 2022 Høgsgaard et al.) 2023) introduced a provably optimal weak-to-Strong learner, establishing robust theoretical foundation for this weak-to strong paradigm. In the field of L.L.s, several studies (Chen et al., Burns et al. (023) have utilized weak models as supervisory signals to facilitate the alignment of LLMs. This paradigm of weak-to-strong generation during training has similarly been investigated in the context of diffusion model training (Chen et al. (025). The research by (Sugiyama al. 2013) recommended directly estimating the density gap between weak and strong models instead of separate estimations. And Auto aitoo-guiance (Karras et al. (024) examines the mechanism of CFG and achieves improved results through interpolation-batt contrast, W2SD utilizes the reflection by leveraging the gap between denoising and inversion to steer generation towards user-defined directions. And we note that W2SD generalizes the concept of idcal model, with experiments across human preference, personalization, fidelity and on, confirming its wide applicability.
perturbation. In
Diffusion Inference Enhancement The study of inference scaling laws in diffusion models has recently become a prominent focus within the research community (Ma et al.] 2025 Ye et al. Liu et al. 2024a Li al. 2026; Shao al.) 2024b Xie et al.). This line of work can be traced back to Re- Rampling (Lugmayr et al. 2022). which iteratively refines latent variables by injecting random Gaussian noise, effectively reverting the noise level to a previous scale. This iterative paradigm has been utilized in subsequent works, including universal conditional control (Bansal al, (023). video generation (Wu et al.) 2023a), and protein design (Jumper al.) [202]) to enhance inference performance. However, has primarily been treated as a heuristic trick, with its underlying mechanisms remaining underexplored. Z-Sampling (Bai et al. (024) extended this paradigm by replacing random noise injection with inversion operations and identified the guidance gap between denoising and inversion as a critical factor. This phenomenon has also been validated in subsequent studies (Zhou et al. 2024 Shao al. 2024a Ahn et al. 2024). In work, systematically unify these inference enhancement methods, demonstrating that their essence lies in approximating the strong-to-iee tronngto--idal gap via the weak-to-strong gap, and integrate them into unified reflective framework, W2SD, through theoretical and empirical analysis.
Reflection Diffusson Model Large language models (LLMs) and multimodal large language models (MLLMs) exhibit the emergent ability to simulate human cognitive processes through reflective reasoning (Cheng et al. 2025 Renze & Guven 2024 Shinn et al. 2023 Shao al., 2025b).
building upon their foundational comprehension and generative competencies. Recent works (Guo
ett al., 2025 Bai et al., 2024 Lou & Ermon 2023 Zhuo et al. 2025) have increasingly focused on integrating the concept of reflection into diffusion models. Z-Sampling (Bai et al. (2024) effectively injects semantic meaning from prompts into the generation process through reflective operations, thereby significantly enbancing prompt alignment. (Pan et al. (025)) effectively incorporates reflective reasoning into reinforcement learning, equipping diffusion models with advanced reasoning capacities. And (Guo al. 2025) pioneered the introduction of reflection mechanisms in autoregressive image
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generation for self- self-correcting unsatisfactory generated images. Particularly, the reflection mechanism has also been applied to image editing in works such as (Jiao et al.) (025) on UnifiedEdit, The "reflected diffusion model" proposed by (Lou & Ermon 2023), reduces numerical errors via reflected stochastic differential equations, while W2SD achieves targeted distribution shifts through dual-model collaboration.
C EXPERIMENT SETTINGS
In this section, we introduce the details of hyperparameters, metrics and datasets used in the experi- ments.
C.I HYPERPARAMETERS
Weight Gap For the W2SD based on weight gap, we consider full-parameter tuning. LoRA-based efficient tuning, and the MoE mechanism.
For the full-parameter tuning, first set SD1.5 (Rombach et al. 2022) as the weak model and the fine-tuned DreamShaper v8 as the strong model, which demonstrates superior performance in terms of human preference and achieves high-quality generation results. Similarly, also use SDXL (Podell et al.) as the weak model and Juggernaut-XL. as the strong model to further evaluate W2SD's performance under weight gaps.
For the efficient tuning, we distinguish strong and weak models by adjusting the LoRA scale. First, use the ArtuuAArtFlllVI LoRA checkpoint quality. Additionally, to validate the ability of W2SD to improve personalization, we select series of personalized LoRAs, as detailed Appendix 0.8, while for the weak model, it is set to -1.5.
W2SD's ability enhance overall image
C.3
For the strong model, the LoRA scale set to
Following the default settings (Bai et al. 2024 we set the denoising steps = 50, and the guidance scale to 5.5. Reflection operations steps X 7 1. Notably, to eliminate influence from guidance gaps, the guidance scale of M and M are both set to 1.0 during reflection, ensuring the guidance gap is zero.
For the MoE (Mixture of Experts) mechanism, we select DiT-MoE-S (Fei et al. 2024) as the strong model, which routes the top 2 optimal experts out of 8 during the inference process. The weak model, in contrast, configured to route the 2 least optimal experts out of 8. Following the default settings, the denoising steps T 50, and the guidance scale is set to 1.5.
Condition Gap In the W2SD research based on condition gaps, we focus analyzing the gaps caused by two mechanisms: guidance scale and prompt semantics.
By adjusting the guidance scale to distinguish the strong and weak model, adapt the same settings as Z-Sampling (Bai et al. 2024); the guidance scale of M was set to 5.5, and the guidance scale of M" is set to 0. The diffusion model used is SDXL.
For semantic gaps, we set M to use the GenEval prompt, which short (4-5 words), ambiguous, and coarse, often resulting in uncontrolled outputs. In contrast, M uses refined prompts enhanced by QWen-Plus (Yang et al. 2024), providing greater detail and semantic richness. During the reflection process, the guidance scale
1.0 to eliminate the influence of guidance gaps on the results.
Similar to the weight gap setup, we set T = 50, À = - 1, and the denoising guidance scale to 5.5.
Sampling Pipeline Gap We demonstrate that W2SD can also generalize to capability gaps across different diffusion pipelines. Specifically, we select ControlNet (Zhang et al. 2023) as M with the control scale set to the default value of 1.0. The standard sampling pipeline (Song et al. 2020 is chosen the weak model. Consistent with the weight gap setup, configure T = 50, x T 1. and guidance scale of 5.5. During reflection operation, the guidance scale for both M and M are set to 0.5 to eliminate the influence of guidance gaps.
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C.2
METRICS
AES. AES (Schuhmann et al., 2022) is an evaluation metric that assesses the visual quality of generated images by analyzing key aesthetic attributes such as contrast, composition, color, and detail, thereby measuring their alignment with human aesthetic standards.
PickScore. PickScore (Kirstain et al. 2023 CLIP-based metric model trained on compre- hensive open dataset containing texl-to-image prompts and corresponding real user preferences for generated images, specifically designed for predicting human aesthetic preferences.
HPS v2. Building upon the Human Preference Dataset v2 (HPD v2), comprehensive collection of 798,090 human preference judgments across 433,760 image pairs, (Wu et al. 2023b) developed HPS v2 (Human Preference Score v2) through CLIP fine-tuning, establishing a more accurate predictive model for human preferences in generated images.
MPS. MPS (Zhang et al. 2024 is metric for text-to-image model evaluation, trained on the MHP dataset containing 918,315 human preference annotations across 607,541 images. This novel metric demonstrates superior performance by effectively capturing human judgments across four critical dimensions: aesthetic quality, semantic alignment, detail fidelity, and overall assessment.
C.3 DATASETS
Pick-a-Pic. The Pick-a-Pic dataset (Kirstain et al. 2023). collected through user interactions with
a dedicated web application for text-to-image generation, systematically records each comparison with prompt, two generated images, and a preference label (indicating either a preferred image or tie when no significant preference exists). Following Z-Sampling (Bai al., (2024), we utilize the initial 100 prompts representative test set, which provides adequate coverage to assess model performance.
Drawbench. DrawBench (Saharia et al. 2022 is a comprehensive evaluation benchmark for text- to- to-image models. featuring approximately 200 text prompts across 1 distinct categories that assess critical capabilities including color rendering, object counting, and generation.
GenEval. Geneval (Ghosh et al. 2024) is an object-focused framework that evaluates image
composition through object co-occurrence, position, count, and color. Using 553 prompts, it achieves 83% agreement with human judgments image correctness.
VBench VBench (Huang et al. 2024) is a comprehensive benchmark for video generation models, featuring hierarchical evaluation framework across multiple quality dimensions. It supports both automatic and human assessment, with VBench++ extending to text-to-video and amage-to-videe tasks while incorporating trustworthiness evaluation.
Peronalization Dataset To evaluate the performance gains of W2SD in personalized generation, we selected 20 LoRA checkpoints from the Civitai platform, covering a diverse range of categories, including persons (e.g. Anne Hathaway, Scarlett Johansson), animals (e.g., Scottish Fold cat, prehistoric dinosaur), styles (e.g., Disney style, parchment style), anime characters (e.g. Sun Wukong, Bulma) and objects (e.g. cars).
D SUPPLEMENTARY EXPERIMENTAL RESULTS
In this section, we present more quantitative and qualitative results of W2SD.
D. QUANTITATIVE RESULTS
Results of W2SD in other benchmarks To further validate the effectiveness of W2SD, also conducted experiments on Drawbench (Saharia et al. 2022). For clarity, we have systematically organized and summarized these experiments in Table In Drawbench, report results based
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Table 8: Quantitative results of W2SD based on full parameter fine-tuning strategy. Our framework generates results better aligned with human preferences. Datasets: Drawbench.
Method
HPS v2
AES f
PickScore
MPS
SD1.5
25.3601
5.2023
21.0519
DreamShaper
28.7845
5.7047
21.8522
47.8813
W2SD
28.7901
5.7847
21.9057
52.1192
SDXL
28.5536
5,4946
22.2464
JuggernattXLL
28. 28.9085
5.3455
22,4906 22.5803
47.5648 52.4358
W2SD
29.3246
5,4261
Table Quantitative results of W2SD based on guidance gap. Model: SDXL. Datasets: DrawBench.
Method
HPS v2 f
AES 1
PickScore 1
MPS
SD1.5 W2SD
25.3601
5.2023
21.0519
47.7075
25.8234
5.2157
21.2079
52.2934
SDXL
28.5536
5,4946
22.2464
40,9590
W2SD
30.1426
5,6600
22.4434
59.0415
Table 10: Quantitative results of W2SD based human preference LoRA model. Our framework generates results better aligned with human preferences. Datasets: Pick-a-Pic.
Method
HPS v2 f
AES
PickScore
MPS
SD1.5
24.9558
5.5003
20.1368
Dpo-Lora
25.5678
5,5804
20.3514
44.2889
W2SD
26.0825
5.6567
20.5096
55.7106
SDXL
29.8701
6.0939
21.6487
XIMoreArtFulli
32.8040
1.76
22.3259
48.2224
W2SD
33.5959
6.2252
22.3644
51.7770
Table 11: Quantitative results of W2SD based on human preference LoRA model. Our framework generates results better aligned with human preferences. Datasets: DrawBench.
Method
HPS v2 f
AES
PickScore
MPS 1
SD1.5
25.3601
5.2023
21.0519
Dpo-Lora
25,8896
5.2895
21.2308
49.3617
W2SD
25.9431
5,3553
21.2589
50.6399
SDXL
28.5536
5.4946
22.2464
XIMoreArFullV1
31.2727
5.5487
22.7721
47.0396
W2SD
32.34857
5.7595
22.8301
52.9588
Additionally, in Pick-a-Pic, on weight gap (see Tables and [T] and guidance gap (see Table 9).
report results based on weight gap (see Table 10). Notably, W2SD demonstrates consistent improvements across all evaluated metrics.
Results of W2SD in Video Generation Task We also validate the performance of W2SD on video generation task to demonstrate its broad applicability. We randomly select 200 prompts from VBench (Huang et al. (024) as test prompt cases and focus on analyzing the AnimateDiff (Guo et al.) video generation model.
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Table 12: Quantitative results of W2SD on the video generation task. Model: AnimateDiff. Datasets: VBench.
Subyact Curaisicncy
Background Cursisicncy
Muticn Smoollanss
Dyuumic Degnaz
Acelactic Quality
Image Quality
Animatzibel (SDXL Animat:DMl (lgg
05.849115
48000199 13,05399
97.54639
96.8833%
57,70975:
64.167499
W250
V1.0386
96.870065
Weak Madal
(SDXL)
Strong Model (xiMorcArtFulll)
W2SD (Weight Difference)
Slipper made potatoes.
little humanlike of deserp..
Gandalf the smoking blun.
Gamer playing loague of legands night.
Figure 15: Qualitative results of W2SD based on weight gaps (human preference). Here we select xIMoreArtFullVI 1 as the strong model and SDXL as the weak model. W2SD can effectively enhance the performance of human preference.
For the strong model MM, we employ AnimateDiff with Juggernaut-XL using guidance scale of 3.0, while the weak model M utilizes AnimateDiff with SDXL guidance scale of 1.0. This setup introduces both weight and guidance gaps, meeting the conditions required by W2SD.
In Table 12 W2SD achieves significant improvements across different dimensions such Subject Consistency. Background Consistency, Aesthetic Quality and mage Quality, confirming its effec- tiveness in video generation task. Notably, the Motion Smoothness dimension, W2SD exhibits performance degradation due JuggernautXXL's inherent limitations compared to SDXL. This observation further validates our theory in Section 3.1
D.2 QUALITATIVE RESULTS
Weight Gap In Figure 15 present visualization results of W2SD based weight gap. Specifi- cally, to enhance human preference for generated images, we select xIMoreArtFullV1 as the strong model and SDXL the weak model.
Additionally, by setting the LoRA-based personalized model as strong model and the un-finetuned base model as weak model, Figure 17 showcases the improvement W2SD in personalized genera- tion effectiveness.
present the visualization results of W2SD based condition gaps. When the strong model utilizes detailed and semantically rich prompts, while the weak model relies simple prompts (containing only 4-5 words), W2SD effectively captures fine-grained grained conditional features. Notably, Z-Sampling (Bai et al., (2024) is a special case of W2SD based on guidance gaps, with extensive visual evidence already provided; thus, omit additional visualizations here.
Condition Gap In Figure 16
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SIXLL
SDXL
S2WD (negative gains)
W25D (positive gains)
S2WD (negative gains)
W2SD (positive gains)
Raw Prompt: photo of black toddy bear.
Raw Prompt:
photo of clocks.
Refined Prompt: heartwarming photograph captures the endearing image of plush black toddy bear, its soft, velvery fur glistening subtly under gentle light, with large, soulful eyes that scem to hold a world of stories and dreams,
Refined Prompt: vintage photograph captures intricate beauty two antique clocks, their ornate faces and polished brass casings reflecting the soft, each ticking synchronized dance time that seems to whisper the secrets the past.
Figure 16: Qualitative results of W2SD based on semantic gaps between prompts, which refines the generation process by placing greater emphasis on the fine-graines details.
Reference Image
Sundand
LoRA
vndgii
Image
Sundeed
LoRA
Bulis
BULMA
Figure 17: Qualitative results of W2SD based on weight gaps (personalization), Here we set LoRA- based personalized model as strong model and the standard model as weak model
Sampling Pipeline Gap In Figure 10 we present the visualization results of W2SD) based on the gaps in the sampling pipeline. By incorporating reference image information through Ip-adapter during the denoising process and employing standard DDIM for inversion, W2SD ensures that the generated image adheres more closely to the given stylistic conditions, resulting in higher-quality results.
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Strong Model
(b) Weak Model
(c) W2SD
(d) S2WD
horse
horse
Figure 18: The CLIP feature corresponding to the generated image x x2xx3xx)) is projected into a 2D space. W2SD effectively disentangles the representations of "car" and "horse". (a) M demonstrates the ability to generate cars; (b) MM can hardly generate cars; (c) W2SD balances the generation distribution, increasing the likelihood of generating cars; (d) S2WD (i.c., My (M"(())) exacerbates the imbalance in data generation.
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W2SD Performance with Few Steps Here also validate the performance of our method under different and T generation settings. In Figure [9] we choose dreamshaper-xl-turts model, using DPM Solver++ the scheduler, and evaluate W2SD based LoRA gap under few steps (T= In Figure 20 we utilize SDXL as the base model, using DDIM as the scheduler, and evaluate W2SD based LoRA gap under multi steps (T=20).
as the base
HPS Performance Scaling with A/T Parameter (To))
HPS Performance Scoling with JuT Parameter (T=20)
22.4
121
10 rerammaa
A7T Ratio
Rabio
Figure 19: HPS Performance Scaling with X/T Parameter (T = 8. daseMoodeddremmshaer xl-turbo. Scheduler: DPM Solver++)
Figure 20: HPS Performance Scaling with X/T Parameter (T = 20). BaseModel.SDXL. Sched- uler: DDIM)
For further analysis, we visualize the denoising trajectories under both few-step (5-step) and multi- step (20-step) settings in a one-dimensional case, as shown in Figure can be observed that the iterative method alternating between weak and strong models achieves effective results in both few-step and nullii-sep scenarios.
One notable observation is that in the 5-step case (top-left subfigure in Figure 21), the trajectory of W2S appears less smooth. Nevertheless, due to the macroscopic consistency in the directional discrepancy between the weak and strong models, the optimized trajectory consistently aligns toward a broadly shared optimization objective.
This finding further reveals that under few-step conditions, the macro-level consistent guidance signal provided by W2SD can effectively steer the sampling trajectory toward more desirable regions in the image distribution.
Srar Heine
Few Stops =
Few Steps T
Strong Model
Cpentten hood
MurH Stops T 20
Walti Shrpps -
Figure 21: W2SD Ensures Effective Guidance Across Sampling Budgets: While 5-step trajectories (top-left) appear less smooth, the macroscopic consistency of guidance steers the sampling process effectively.
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Analysis of the Limitations and Failure Scenarios in W2SD In Theorem that the weak-to-strong gap cannot consistently serve as reliable proxy for the strong-to-ideal gap. This limitation manifests in two typical scenarios: model conflict and model over-similarity. Representative examples of these failure modes are illustrated in Figure 22 and Figure 23 respectively,
demonstrate
Taking Figure 22
example, here M1 represents model associated with the "Disney Style", while M2 corresponds to the "Ink Style". Our goal was to generate a Disney-style dog in ink wash painting; however, this objective could be achieved regardless of whether Mi or M2 was used as the strong model. This failure stems from the fact that such model pair is not well-defined for the task of generating "Disney-style ink paintings."
As Strong Model
As Weak Model
(b) M₁- Lorn (Disney Style)
My- Lorn (Roalsste)
Ma- Lora (NorAte)
M₁- Lora (Ink-Shyle)
realistic portrait Naruto. rendered extremely fine detail with hyperrealistic skin texture and authentic costume elements.
close-up portrait rendered the expressive style of ink wash painting. with fluid black brushstrokes and gradient grey washes.
Disney-style dog.
Figure 22: Failure Scenario 1: Model Conflict. W2SD fails when weak and strong models have mutually exclusive features.
Moreover, when the capabilities of the models in the model pair too similar, the resulting model gap becomes too weak and lacks a clear directional signal. In such cases, W2S fails to provide meaningful performance gains. In Figure 23 we selected two similar preference LoRAs (specifically XlMoreArtFullV and styleLoraRealis). Due to the marginal capability gap between them, the optimization effect remains notably weak and highly anconsistent-whiee some cases (e.g.. bottom-right in Figure 23 show slight improvement, others (e.g., top-right) exhibit clear performance degradation.
M
M2
W2SD
M
M2
W2SD
M,
M2
W2SD
Figure 23: Failure Scenario 2: Model Over-Similarity. W2SD yields limited gains when weak and strong models possess highly similar features, resulting in a weak guidance signal. Here, M, (strong model) corresponds to xfMureAnfullVV,, while M2 (weak model) corresponds to Ltyael.raReells.
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Analysis of the Reward Model-Based W2S Variant We now present variant of the W2S approach (Please see Algorithm 2) which leverages a reward model (c.g.. HPS or PickScore) to automatically designate the strong and weak models at each step. This variant addresses the key limitation of fixed model pairing by introducing dynamic selection mechanism. At each denoising step, the reward model performs real-time assessment of the intermediate outputs from both models. The model that generates the higher-scoring output is automatically designated as the "strong" model for that particular step, while the other serves the "weak" model.
strong: Ma weak: M;
strong: weak: M₂
W2SD-Variant (auto-selection)
M
M
(b)
(c)
Figure 24: W2SD selecselection provides flexibility by climinating the need for pre-defined models (a, b), but fails when models are too similar to offer meaningful guidance (c).
To validate this perspective, we experiment with two related, preference-aligned LoRA weights g
(M' M We compare the standard W2SD (Algorithm against the dynamic variant (Algorithm 2 on the same model set under identical conditions, with results shown in Table [3] We present the visualization results in Figure
Algorithm W2S with Dynamic Model Selection
I: Input: Model Mi. Model MM, Total Steps: T. Evaluation Metric: & (e.g., HIPS, PickScore), Threshold
Output: Refined Data Xo
3: Initialize Xr (Sample from Gaussian noise)
4: for / to do
5: # Dynamicc Model Selection
C: t (x,,,,,, c² + 2 (x:,t)
7:
r1 + E(ci), r2 + E((2)
8:
if > r2 and | r2 > 6, then
9:
M + M _ M
10:
else
M M² M M!
12:
end if
13:
W2SD with Reflection
14:
R; + (M,
15: X --i+Mar Mx,,x,
16: end for
17: return xo (Final refined data)
SSpecifically, XIMoreArtFullVi and AlMorAArtFllllee from Civitai.
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Table 13: HPS v2 evaluation of individual models and W2SD variants. Experiments conducted on curated set of 20 prompts from the Pick-a-Pic dataset.
M'
M²
('(MEn))
M (W2SD)
Auto-Selection
(Single)
(Single)
(W2SD)
(W2SD)
HPS v2 t
30.16
26.66
27.16
30.29
30.89
E MECHANISM ANALYSIS AND UNDERSTANDING
E.1 W2SD IN CIFAR-10
In this subsection, we investigate the performance of W2SD real image data. For ease of analysis, we select two classes from CIFAR-10 10 (Krizhevsky et al. 2009): car and horse. Specifically, we train the weak and strong diffusion models on distinct datasets. For M the dataset consists of 5,000 horse images and 2,500 car images. For M it comprises 5,000 horse images and 500 car images. In this scenario, due the imbalance in training dataset, both M and MM are more inclined to generate horses. Moreover, since M is trained on a limited number of car images, it rarely generates cars.
In Figure 7 we note that W2SD can help balance the image categories, enhancing inference process to increase the probability of generating cars. In Figure T8 we also perform a t-SNE dimensionality reduction (Van der Maaten & Hinton 2008) on the CLIP features of the generated images. W2SD effectively disentangles the representations of "car" and "horse" in the 2D space. Notably, the ratio of "horse" to "car" under W2SD approaches 1:1. In contrast, applying the negative reflection operator Miny (MM")) worsens the data imbalance, validating the effectiveness of our framework.
E.2 VISUALIZATION ANALYSIS
To provide a more intuitive demonstration of the W2SD effect, we present more 1D visualization examples in Figure 25 to aid understanding. As can be seen, W2SD has certain probability of "correcting" the denoising trajectory of the model, resulting in more balanced generation outcomes. The settings here are consistent with those in Figure 5
We also empirically validate that the weak-to-strong gap A2 can effectively bridges the strong- to-ideal gap A₁. We first compute CosineSimilarity (A (t). Az(t)) at each timestep We train three models on CIFAR-10: the weak model (100 epochs), the strong model (300 epochs), and the ideal model (fully converged, 500 epochs). Here (t) = (idea(()) Estrong (t) and (t Estrong (f) (weak(() (f). In the table below, the angle between A1 and (2 remains below 90" confirming that weak-to-strong gap can reliably bridge strong-to-ideal gap.
To further validate this claim that A₂ can bridge AI, provide additional visualizations. As illustrated in Figure 27] the W2SD trajectory is visualized in 2D space, where its denoising direction (black) demonstrates closer aligmment with the ideal direction (green). Moreover, the angles between the strong (red)-to-wel weak (blue) and ideal ggreen)-to-strong (red) vectors consistently remain within 90 9
E.3 THE IMPACT OF APPROXIMATION ERROR IN THE INVERSION PROCESS
In Section 2 we assume that the inversion and denoising process are reversible, meaning that for the same generative model (including the same guidance scale, etc.), Mine (MM 4), () Tt. However, in practice, the inversion process inevitably introduces errors. Specifically, for 2, at time t, the inversion process actually used in the algorithm implementation as
i Zt-A:
21 se (o:I--r, 21 (5o -
(32)
Ft At
so (x,, +.8 (2e, (fr, AI,
(33)
Inversion Error E,
And the effect of W2S the latent variable in Theorem can also be expressed as
ft mt 21 A((V,, (x))) log P. (are) Ex),
(34)
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Figure 25: Denoising trajectories across different settings (I-D Gauss). The weak model (blue) generates only right-peak data due to missing left-peak training samples, while the strong model (red) produces data between both peaks. W2SD balances the distribution by leveraging the reflective operator MW luy (-).
Similarity (Eatrong Estrong)
Similarity (Eweak-Estren Estrong)
Cosine Similarity Score
0.4
0.2
0.0
-0.4
-0.6
Timesteps
Figure 26: Positive cosine similarity between A and A2 (cos θ << 90%)
where Inversion Error E, represents the approximation error in the inversion process at time (. Since At is very small, sp(2,, t) and sy (I t) are assumed to be approximately equal by default, i.c. E, s 0.
To further analyze the impact of E, on the W2SD, we simplify the analysis by replacing E, with Gaussian noise of controllable magnitude as
f + x² At(V log
V v., log (xx) kc).
(35)
By varying the value of k. adjust the magnitude of the emror E, to study its effect on the generated results. We analyze W2SD based on weight gaps, with the strong model using xIMoreArt-Fulle and the weak model using SDXL.
In Table 14 as & increases, indicating larger approximation error E,, the gains from W2SD diminish. This finding is consistent with 7-Sampling (Bai et al., 2024 results, demonstrating that
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Diffusin Trajectoniess
Diffusion Trsjectories
11
-0.5
Diffusion Trajectories (w2sd)
11 3.5
10000g
11
11 -1.0
5
Start point
3.0
End point
arong
-2.0
-2.5
1.5
1.0
-5
-3.5
0.5
15
-10
5
0
5
10
Diffusion Trajectories
4.0
k
< or
-4.5
11
ideal #2ad
4,(0)
11
2.0
Figure 27: 2D denoising path visualization. The weak-to-strong gap can effectively bridge the strong-to-ideal gap.
Table 14: As the magnitude of the approximation error in inversion process increases, the gains from W2SD diminish. Model :xMMorcArFullVII Datasets: Pick-a-Pic. The type of W2SD: weight gap.
Method
HPS v2 f
AES +
PickScore t
MPS +
SDXL xIMoreArtFullV1
29.8701
6.0939
21.6487
32.8040
6.1176
22.3259
48.2224
W2SD (k=0)
33.5959
6.2252
22.3644
51.7770
W2SD (k=0.005)
32.9341
6.3228
22.3221
46.7130
W2SD (k=0.010)
19.5277
4.3949
17.9267
1.3440
this phenomenon occurs in both guidance gap and weight gap scenarios, indicating that minimizing the approximation error in inversion process is crucial.
E.4 RELATIONSHIIP WITH ITERATIVE SAMPLING
Re- Se-Sampling Lugmayr et al. 2022) stands as the pioneering iterative sampling algorithm in diffusion models. Numerous subsequent approaches including FreeDoM (Yu et al., (202)) and UGD (Bansal et al. 2023) have been developed based on this foundational work. We argue that these methods represent specialized instantiations the W2SD framework.
We first confirm that Re-Sampling is generally specific instance of W2SD, which can be interpreted within the framework of our theory in Theorem | better when the randomly sampled Gaussian noise in Re-Sampling is similar to the perturbation vector introduced by the W2SD reflection mechanism (e.g., cosine similarity > O). Additionally, propose advanced version of Re-Sampling (see Algorithm 4 which evaluates whether the similarity score, sim www.sccorees.. c), exceeds to determine whether the Gaussian noise should be accepted for the ReNoise operation.
Figure we note that Re-Sampling performs
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Table 15: By selecting Gaussian noise during the Re-Sampling process, the ad- vanced Algorithm achiivess superior performance in the sampling process, demon- strating that Se-mmmmling specific instance of W2SD. Model: SDXL. Datasets: Pick-a-Pic. The type of W2SD: guidance gap.
Method
HPS v2 f
AES
PickScore 1
MPS t
SDXL
29.8701
6.0939
21.6487
Re-Sampling (sim score<0))
30.2797
6.0744
21.6894
48.4793
Re-Sampling (sim score>())
30.7844
6.0555
21.8620
51.5210
W2SD
31.2020
6.0970
21.7980
56.0608
MM in W2SD
RaNalso
(any So0e ()
Bad Renoise
Good Remoise
sim score<()
( sim score>0)
X X1-4t
X₁
Figure 28: Re-Sampling, which can be consid- ered specific instance of W2SD, demonstrates improved performance when the randomly sam- pled Gaussian noise aligns closely with the per- turbation vector introduced by the W2SD reflec- tion mechanism (e.g., cosine similarity 0)
Figure 29: Qualitative results of advanced Re- Sampling demonstrate that the improvements effects vary depending on the strategy used to select Gaussian noise for Re-Sampling. can be considered specific instance of W2SD.
We validate the effectiveness of Algorithm 4 in Table 15 When consistently selecting favorable random noise (i.c., Ew2s, e) > 0), advanced Re- Re-Sampling demonstrates improved performance. Con- versely, when consistently selecting unfavorable random noise (i.e., sim score((w2s> c) 0), the performance of Re-Sampling deteriorates. We also present the visualization results in Figure 29 further demonstrating that Re-Sampling be incorporated into the W2SD framework, validating the correctness of our theory in Theorem
Similarly, many subsequent research, such FreeDoM (Yu et al. 2023), UGD (Bansal et al. 2023) MPGD (He et al. 2023), and TFG (Ye et al., 2024), follow the same approach as Re-Sampling by utilizing random Gaussian noise for iterative optimization. Therefore, these inference enhancement methods can be regarded as specific instances of W2SD. The primary distinction among these methods lies in the specific strong model M they employ. For instance, TFG utilizes a more refined parameter search mechanism, resulting in strong model that exhibits greater robustness and performance compared to algorithms such as FreeDoM and UGD. As a consequence, under the condition of the same weak model (i.e.. the addition of random Gaussian noise), TFG demonstrates significantly enhanced performance. However, these studies collectively overlook fundamental aspect: the seak-to-strong gap constitutes the core principle that fundamentally drives the efficacy of such algorithms.
E.5 RELATIONSHIIP WITH AUTO-GUIDANCE
We note that in the weak-to-strong framework, Auto-guidance (Karras et al.) 2024) employs pre-trained diffusion model along with a corrupted version of it (typically achieved by adding perturbations reducing training iterations through training from scratch). It directly enhances
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Algorithm 4 Advanced Re- Se-Sampling
Input: Strong Model M Weak Model MM,
Total Inference Steps: T, Optimization Steps:
À
Algorithm 3 Vanilla Re-Sampling
Output: Clean Data JD Sample Gaussian noise 2T for to 1 do
Input: Strong Model M Total Inference
Steps: T. Optimization Steps: À
Output: Clean Data
if / T then
Sample Gaussian noise ZT
21 -M
for t T to do
2, MM (2)
if > T then
<w2; = It It
Tt-1 (M
Calculate 6w2s based Equation (
Initialize e ~ (0, 1) 2, Add Nois
#Select Optimal ReNoise
Initialize (0,
end if'
while similarity_ (Ew2s E) < 0 do
21-1
(1
Initialize ~N(00,
end for
end while
zRRe
AAdd__Nois Add_NoisseMi,
end if
Ft-1 = (M
end for
performance by interpolating in the latent space. And here we clarify the contributions of W2SD in relation to it.
Different mechanisms W2SD employs an reflection mechanism, while Auto-guidance utilizes interpolation- method. For comparison with W2SD, set w=1 in Auto-guidance. When using Strong Model (human preference model) vs Weak Model (SDXL). Table 16] we show that W2SD achieves notably higher scores human preference metrics including PickScore and HPS v2. However, in this setting, direct interpolation in Auto-guidance leads to performance degradation in certain metrics, manifesting as oversaturation and artifacts. Actually, the auto-guidant iitidgguiancee mechanism similarly utilizes the following operations as
F4 > good
(36)
31 - bad
(37)
2--1 xt-1
good
(=1-1
xx-1)
(38)
When is too large, applying Equation (38 roughly refines the distribution of the latent variables,
leading to unnatural shift in the data distribution (Sadat et al. 2024 Lou & Ermon too small, it fails to produce sufficient refinement.
2023).
When
Table 16: Performance comparison between Auto auto-guidance's interpolation and W2SD's reflection mechanism in latent variable refinement.
Method
HPS v2 f
AES A
PickScore f
SDXL
29.8701
6.0939
21.6487
X/MorVAAFFullVI
32.8040
6.1176
22.3259
Auto-guidance
32.1650
6.1187
22.0177
W2SD
33.5959
6.2252
22.3644
In W2SD's process, Zt 2t-1 + Ft, the refinement operation (marked in red) is implicitly per- formed by score network's 's internal transformation which avoids common artifacts like distortion and over-saturation, please see Figure 30
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Auto Guidance
NATUCNUEX MIK REAL REAL
W2SD (Ours)
MIRCI
Figure 30: Compared with Auto-gum gutto-guidacee, W2SD achieves superior performance with enhanced robustness, effectively addressing critical issues such as oversaturation and optimization failure.
Flux
WZ5D (Ours)
Ealanced lighting
Ricker desails
Better composition
Preferred saturation
Figure 31: Visual Case of W2SD (Flux vs SDXL). W2SD can support cross-architecture operations (c.g., DiT and UNet).
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Flux (sub optim ofg)
Flux (standard cfs)
Flux (W2SD)
Flux (No LoRA)
Flux
Flux (W2SD)
(Human Preference LoRA)
Hatsune es REAL
LS REAL
The results of W2SD Guidance Gap based on FLUX.1-dev
The results of W2SD LoRA Gap based on FLUX.1-dev
Figure 32: Flux model results: W2SD bridges the performance gap between weak and strong variants.
Varying Applicability Ranges On the other hand, we note W2SD generalizes the concept of weak/strong model pairs-where the "weak" model is not limited underperforming variants created through reduced capacity or training strategies (e.g., data corruptions or degradations as in Auto- guidance). We propose that gaps in semantic interpretation of prompts or sampling methodologies (e.g., MoE routers, ControlNet adaptations) can equally constitute valid weak-strong pairings. This expanded paradigm demonstrates significantly greater practical utility, as it accommodates real-world deployment scenarios where model capabilities vary along multiple axes.
Cross-architecture Support Compared to Auto-guidance's s direct interpolation approach, we demonstrate that W2SD's reflection mechanism enables coss-architecture operations in pixel space (mapping Iy to pixel space (rn), applying W2SD, and projecting back to latent space).
We select Flux the strong model (latent shape: [1,16,128, 128)) and SDXL as the weak model (latent shape: [1,4, 128, 128]). Despite the differences in latent shapes between Flux and SDXL, we note that W2SD can support cross-architecture operations in the pixel space (mapping 2 pixel space Tn). applying W2SD, and projecting back to latent space). In this configuration, we show that W2SD could improves image quality, with Figure 31 demonstrating superior lighting, detail preservation, better composition and preferred saturation. The image quality winning rate of W2SD up to 74%. This suggests W2SD exhibits noos-architecture/daaa generality.
F.6 EXPERIMENTS ON FLUX
In this section, present supplementary experimental results of W2SD using Flux the base model. Specifically, Table 17 and [8 report the results two variants of W2SD, namely the guidance gap and lora gap. For the guidance gap variant, the weak model is model to CFG=2.0. For the LoRA gap variant, the weak model is the base model without any LoRA modules, while the strong model incorporates LoRA modules with scale of 0.3. The total number of denoising steps 7' is 28, with the reflection window X set to 10. Furthermore, we provide qualitative comparisons of the generated samples in Figure 32
CFG=1.0 O and the strong
Table 17: Quantitative results of W2SD based on FLUX. Datasets: Pick-a-Pic.
Method
HPS v2
AES
PickScore 1
Flux (sub-optimal cfg)
23.2291
6.0081
20,5669
Flux
29,9532
6,3668
22.1578
W2SD (based on guidance gap)
31.1962
6.3677
22.2464
Flux LoRA)
30.3402
6.3987
22,2199
W2SD (based on lora gap)
31.7411
6.3580
22.3050
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Table 18: Quantitative results of W2SD based FLUX.1-dew, Datasets: DrawBench.
Method
HPS v2
AES f
PickScore f
Flux (sub-optimal cfg)
22.5098
5.5170
21,4877
Flux
29.2550
5.8035
22,8866
W2SD (based on guidance gap)
30.6314
5,9030
23.0236
Flux LoRA)
29.5438
5,8088
22,8680
W2SD (based on lora gap)
30.9390
5.9238
22,9202
37


Reviews:
[{"review_id": "tcLgDfVEvR", "reviewer": "Reviewer_RUsL", "summary": "The paper introduces Weak-to-Strong Diffusion (W2SD), an inference-time method that alternates between denoising with a strong model and inverting (i.e. adding noise back) with a weak model. Using the weak-to-strong gradient gap ($\\Delta_1 = \\nabla \\log p_s  - \\nabla \\log p_w$) to approximate the strong-to-ideal gap ($\\Delta_2 = \\nabla \\log p_{\\text{data}}  - \\nabla \\log p_s$) the authors demonstrate a training-free to improve sampling using a variety of different weak/strong model pairs.", "questions": "**(Q1)**: The term \"reflective operator\" is not well-justified. The operation $x_t = M_{inv}^{w}({M}^{s}(x_{t},t))$ is a \"denoise-then-invert\" step that applies a correction. The paper doesn't explain what is being \"reflected\" or from what surface/manifold. \n\n**(Q2)**: When does $\\Delta_1 \\approx \\Delta_2$ hold? Under what theoretical settings or formalized assumptions? \n\n**(Q3)**: Are there simple, training-free heuristics to pick the weak and strong models, or the reflection window?\n\n**(Q4)**: Could the authors report actual wall-clock time on a fixed GPU and per-image variance across seeds for several $T$ and $\\lambda$?\n\n**(Q)**: There are many minor typos (e.g., \"applues,\" \"socre,\" \"proivde\"), and sometimes ambiguity around whether $s_{\\theta}$ is a score or an $\\epsilon$-predictor.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "**(S1)**: The approach is simple and training-free, and can flexibly be used with various different models.\n\n**(S2)**: Experimental results explore a variety of different diffusion models and architectures.\n\n**(S3)**: A discussion on compute-aware sampling is provided, with considerations for sampling quality within a fixed wall-clock budget. This is relevant for broader applicability.", "weaknesses": "**(W1)**: The proof of Theorem 1 is weak. There is no solid justification given to \"neglect the approximation error\" (L727). The proof ignores Jacobian terms or any formulation for the approximation error. No conditions are provided for when $\\Delta_1 \\approx \\Delta_2$. Omitting these conditions is a significant weakness. This makes the justification more heuristic than theoretical.\n\n**(W2)**: The authors note that when the gap magnitude is negative (i.e. strong model weaker than the weak model), quality degrades (L440). There are no provided principled diagnostics or automatic safeguards to prevent harmful pairings or schedules. This leaves automatic model-pair selection an open practical issue of the method.\n\n**(W3)**: Incomplete baselines. There are strong, training-free inference baselines are only discussed but not thoroughly compared in tables: e.g., Auto-Guidance, Z-Sampling variants, TFG, other schedule- or guidance-optimization methods. Many tables compare only “base vs W2SD\". These omissions cloud discussions of relative merit.\n\n**(W4)**: Computational cost. The results in Figure 13 rely on a setting where $T_{w2s}$ is halved and $\\lambda$ is small. There are multiple experiments in the appendix, however, that state $\\lambda = T-1$, which implies the reflection operation (that uses two model passes) is performed at nearly every step according to Algorithm 1, effectively doubling the inference cost. Ablations on the reflection window and schedule are limited.\n\n**(W5)**: Hyperparameter tuning. Based on Figure 11, hyperparameter choices can significantly influence quality. If the gap is negative due to poor choices for LoRA scales, guidance scales, or expert selection, then performance may not be good. This might require extensive tuning, which takes away from the \"training free\" approach of the paper.\n\n**(W5)**: Omission of comparisons with “Reflected Diffusion Models.” The empirical and conceptual separation from related work like reflected diffusion models could be made more explicit.\n\nOverall, the weaknesses outweigh the strengths. The paper would benefit from stronger baselines and a clearer theoretical justification.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "HAHSdzVzL4", "reviewer": "Reviewer_DEkr", "summary": "This paper introduces Weak-to-Strong Diffusion (W2SD), a novel, training-free framework designed to enhance the performance of pre-trained diffusion models at inference time. The core idea is to leverage the \"weak-to-strong gap\"—the difference in score estimates between a capable (strong) model and a less capable (weak) one—as a proxy for the unattainable \"strong-to-ideal\" gap. The authors propose a reflective sampling mechanism, which alternates between denoising with the strong model and inverting with the weak model, to steer the sampling trajectory towards the true data distribution. W2SD is presented as a general meta-framework, and its effectiveness is demonstrated across a wide variety of \"weak-strong\" pairings, including gaps in model weights, conditional inputs (e.g., CFG scale, prompt quality), and sampling pipelines, showing consistent improvements on both qualitative and quantitative benchmarks.", "questions": "1. Regarding the mechanism itself: Could a simpler \"difference guidance\" approach work as well? For example, at each step, one could compute the predicted noise from both models, $\\varepsilon_s$ and $\\varepsilon_w$, and form a new prediction $\\varepsilon_{\\text{final}} = \\varepsilon_s + \\alpha \\cdot (\\varepsilon_s - \\varepsilon_w)$, where $\\alpha$ is a guidance scale. This seems to capture the same core idea but avoids the model inversion step. How does the proposed reflection operator compare to such a baseline?\n\n2. Regarding the visualizations in Figures 3 & 4: Could you provide more specific details on how these plots were generated? For instance, how were the probability densities for the \"Ideal,\" \"Strong,\" and \"Weak\" models in Figure 3 obtained? For Figure 4, what were the specific data distribution ratios used to train the models to induce the bias? This would improve the reproducibility and clarity of this excellent intuitive demonstration.\n\n3. Regarding the definition of \"weak-strong\" pairs: The paper shows many successful pairings. From your experience, are there examples of model pairs that are difficult to define as strictly \"weak\" or \"strong,\" or pairs that failed to produce improvements? For example, what if one model is better at global composition but worse at fine details, while the other is the opposite? A discussion on such challenging or failure cases would provide a more complete picture of the framework's boundaries.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Simple, Effective, and General Idea: The core concept of using the difference between a weak and a strong model to approximate the direction of improvement is both intuitive and powerful. The framework's ability to operate on various types of \"gaps\" (weight, condition, etc.) demonstrates its impressive versatility.\n\n2. Strong and Comprehensive Empirical Results: The paper provides extensive evidence of W2SD's effectiveness across multiple models (SD1.5, SDXL, DiT), tasks (image, video), and metrics (human preference, prompt adherence). The cumulative effect shown in Table 7 is particularly compelling.\n\n3. Excellent Clarity and Presentation: The authors have done an outstanding job of explaining a complex idea in a clear and accessible manner. The writing and visualizations significantly aid in understanding the method's mechanics and motivation.", "weaknesses": "1. Idealized Assumption of the \"Weak-to-Strong\" Gap: The framework's core assumption is that the weak-to-strong gap vector is a reliable proxy for the strong-to-ideal gap. While this holds in the controlled 1D/2D experiments where models differ mainly in data bias, it may be too idealized for real-world scenarios. In practice, a strong and weak model may have qualitatively different failure modes or \"worldviews\" due to differences in architecture or fine-tuning data. In such cases, their difference vector could be noisy or even misaligned with the true direction of improvement. The paper could benefit from a discussion of this limitation.\n\n2. Necessity of the Reflection Mechanism: The proposed reflective operation (denoise-then-invert) is elegant, but it is not immediately obvious if this complexity is necessary. A simpler alternative, such as directly guiding the strong model's prediction with the difference vector, might achieve similar results with less computational overhead. The lack of comparison against such a baseline makes it harder to isolate the contribution of the specific reflection mechanism.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "TSMJSUaZyf", "reviewer": "Reviewer_99Dw", "summary": "This paper introduces Weak-to-strong diffusion models (W2SD), an inference‑time framework that uses a reflection operator combining a strong diffusion model (M_s) and a weak model (M_w) to push samples along the estimated weak‑to‑strong gradient gap.\n\nThe proposed framework is flexible in choosing weak/strong pairs, including weight gaps, condition gaps, MoE routing gaps, and pipeline gaps. Experiments cover text‑to‑image, personalized LoRAs, and even video generation, showing consistent improvements and cumulative gains across gaps", "questions": "- How does W2SD compare to Auto‑Guidance and Z‑Sampling **under matched compute** across diverse prompts (quantitatively)?\n- Does repeated reflection risk **mode collapse** in long runs (i.e., is there guaranteed convergence?)? \n- Theoretically, how to justify or prove the claim of bridging the strong-to-ideal gap with the weak-to-strong gap? \n- How to precisely define a weak, strong, and idea model in the framework, for example, for specific scenarios, a common weak model can be \"strong\".", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- The unified W2SD is general and applicable to different diffusion models. \n- Strong results covering different regions of interest.", "weaknesses": "Overall, the presentation of this paper is a problem. There are many figures and tables in both the main paper and the supplementary. However, the authors failed to organize them well in the text, making the paper slightly hard to read. A few concrete comments include: \n- Figure 2 is hard to understand. No further explanations are associated with it. \n- Algorithm 1 did not show anything specific about the W2SD algorithm, but a widely used procedure for inference-based optimizations. \n- Eq 5 and the sentence below it are inconsistent, i.e., no \\delta_1(t) at all. \n- Also, Eq 5 cannot be called a \"Theorem\". Even with Section A in the Appendix, altogether they are a definition but not a strict proof. \n- l135-137: It is unfair to treat Z-Sampling (Bai et al., 2024) and other similar methods as instances of W2SD.\n\nOther weaknesses: \n- Comparison to stronger baselines. For most of the experiments, the authors compare the W2SD version with the corresponding baseline model. It is also better to include other baselines. For example, with W2SD, can we tweak SDXL to Flux? \n- Mathematical support for the correctness of W2SD is missing.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "D9lFSyJwsM", "reviewer": "Reviewer_Xkjj", "summary": "This paper introduces a new approach to minimize the gap between the learned probability distribution and the actual probability distribution(intractable) of data. This uses the divergence of distribution of a weak model and a strong model as the proxy for divergence of real and learned distributions.", "questions": "1. What is the increase in computation for this method as compared to the SOTA methods such as Z-sampling, AutoGuidance etc?\n2. What is the relation between the values of $\\mathcal{T}$ and $\\lambda$? How are these decided based on the models? A discussion on this would be helpful as to how these parameters handles the proxy.\n3. Since LoRA like techniques are used for personalization i.e., to bias a model towards a specific distribution, what is the intuition behind considering the model strong? Strong in what terms?", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "1. Simple and general idea with practical reach. Using the difference between a weak and a strong model as proxy for the actual difference between real and learned distribution seems to be fair given the assumptions in the paper.\n2. The W2SD algorithm is backed by various experiments, showcasing that it can be practically used with pretrained models.", "weaknesses": "1. The central claim is that the weak-to-strong gap $\\Delta_1$ is a useful proxy for the intractable strong-to-ideal gap $\\Delta_2$. The paper provides cosine-similarity evidence on CIFAR, but this may not generalize: for some kinds of differences (e.g., when $M_w$ is biased towards different modes than the ideal), $\\Delta_1$ might be orthogonal or adversarial to $\\Delta_2$. The presented sensitivity analyses (gap sign and magnitude) indicate failure modes, but there is not a principled rule for selecting pairs to guarantee positive gains.\n2. Even though the method shows gains in various quantitative scores, the increase in computation is not described in paper and is an important factor when comparing with techniques such as Z-sampling, AutoGuidance, CFG, etc.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "SwYHdwTcvJ", "reviewer": "Reviewer_nwAH", "summary": "- This paper introduces Weak-to-Strong Diffusion (W2SD), a novel, training-free framework designed to enhance the performance of diffusion models during inference. The core problem it addresses is the \"modeling gap\": the discrepancy between the data distribution learned by a diffusion model and the true, ideal data distribution.  \n- Essentially,  instead of trying to directly estimate this unattainable \"strong-to-ideal\" gap, W2SD leverages a more accessible proxy: the \"weak-to-strong\" gap. This is the difference in behavior between a high-performing \"strong\" model (e.g., a fine-tuned model like Juggernaut-XL) and a lower-performing \"weak\" model (e.g., a base model like SDXL).  \n- The framework operates through a reflection mechanism. During sampling, it alternates between:\n  - A denoising step using the strong model (to move towards a high-quality output).  \n  - An inversion step using the weak model (to add back a controlled amount of noise, effectively \"reflecting\" the latent variable).  \n- A key contribution is the broad definition of what constitutes a \"weak\" and \"strong\" model. The paper demonstrates three types of gaps:\n  - **Weight Gap:** Different model weights (e.g., SD1.5 vs. DreamShaper, base model vs. a LoRA-adapted model, strong vs. weak experts in a Mixture-of-Experts model).\n  - **Condition Gap:** The same model under different conditions (e.g., high vs. low classifier-free guidance scale, detailed vs. simple text prompts).  \n  - **Sampling Pipeline Gap:** Different inference pipelines (e.g., ControlNet/IP-Adapter vs. standard DDIM sampling).  \n\n  As shown in the paper, when combined, they usually yield better results.  \n\n- Extensive experiments across image and video generation tasks show that W2SD consistently improves performance on metrics like human preference (HPS v2, PickScore), aesthetics (AES), and fidelity (FID), often outperforming related methods like Auto-Guidance and Z-Sampling. Crucially, the performance gains are shown to outweigh the additional computational cost, making W2SD efficient under equal time constraints.", "questions": "- How does this method perform when using a smaller number of diffusion steps? Does the assumption of the smoothness of the score degrade the generation performance?  \n- Is it possible to theoretically justify this improvement?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "- The paper is well written and easy to follow.  \n- **High Flexibility and Generality:** W2SD is not a single technique but a meta-framework. Its ability to incorporate various types of model pairs (weights, conditions, pipelines) makes it widely applicable across many use cases without retraining.  \n- **SOTA Empirical Results:** The paper provides comprehensive quantitative and qualitative evidence across multiple benchmarks (Pick-a-Pic, DrawBench, ImageNet), architectures (UNet, DiT), and tasks (image, video generation), demonstrating consistent and significant improvements.  \n- **Training-Free:** As an inference-time method, W2SD can be readily applied to existing models and pipelines without the need for costly additional training.  \n- **Diverse evaluation:** The method is tested on many datasets, different diffusion models, and various types of diffusion use-cases.\n- **Ablation Studies:** The method is properly analyzed on both synthetic and real data cases. Each part of the method is thoroughly interpreted, highlighting its effectiveness. Additionally, a toy test is shown in the paper (Figure 6), demonstrating the benefit of the method, where failure cases of both the strong and the weak models were exploited to produce pleasing-looking images of cars.", "weaknesses": "- The contribution of the result from Theorem 1 is minimal: It states a very naive result, without adding any contribution to the paper or supporting the method's effectiveness in any way.  \n- The method assumes that the score function is very smooth w.r.t. t, specifically the approximation in (4). This might be a limiting factor of the method in accelerated diffusion setups, where the jump between two consecutive steps is more significant.  \n- The method is not supported by theoretical justification.  \n- Performance Degradation: If the weak-to-strong gap is not a good proxy for the strong-to-ideal gap (or is even negatively aligned), the method can lead to worse results than the strong model alone.  \n- Limited Exploration of Limitations: Some practical limitations are mentioned only briefly in the appendix. A deeper discussion of failure modes or scenarios where W2SD is not applicable would be beneficial.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)