Title: Transfer Learning for Diffusion Models
Venue: NeurIPS 2024
Accepted: yes
Keywords: Diffusion Model

Transfer Learning
Abstract: Diffusion models, a specific type of generative model, have achieved unprecedented performance in recent years and consistently produce high-quality synthetic samples. A critical prerequisite for their notable success lies in the presence of a substantial number of training samples, which can be impractical in real-world applications due to high collection costs or associated risks. Consequently, various finetuning and regularization approaches have been proposed to transfer knowledge from existing pre-trained models to specific target domains with limited data. This paper introduces the Transfer Guided Diffusion Process (TGDP), a novel approach distinct from conventional finetuning and regularization methods. 
We prove that the optimal diffusion model for the target domain integrates pre-trained diffusion models on the source domain with additional guidance from a domain classifier. 
We further extend TGDP to a conditional version for modeling the joint distribution of data and its corresponding labels, together with two additional regularization terms to enhance the model performance. We validate the effectiveness of TGDP on both simulated and real-world datasets.

Transfer Learning for Diffusion Models

Abstract

Diffusion models, a specific type of generative model, have achieved unprecedented performance in recent years and consistently produce high-quality synthetic samples. A critical prerequisite for their notable success lies in the presence of a substantial number of training samples, which can be impractical in real-world applications due to high collection costs or associated risks. Consequently, various finetuning and regularization approaches have been proposed to transfer knowledge from existing pre-trained models to specific target domains with limited data. This paper introduces the Transfer Guided Diffusion Process (TGDP), a novel approach distinct from conventional finetuning and regularization methods. We prove that the optimal diffusion model for the target domain integrates pre-trained diffusion models on the source domain with additional guidance from a domain classifier. We further extend TGDP to a conditional version for modeling the joint distribution of data and its corresponding labels, together with two additional regularization terms to enhance the model performance. We validate the effectiveness of TGDP on both simulated and real-world datasets.

1 Introduction

Diffusion models have achieved remarkable success in modeling data distributions and generating various types of synthetic data, such as images [13, 36, 17], videos [14], vision language [32, 33, 30], and time series [39]. However, their success heavily relies on the availability of a large number of training samples. In real-world applications, acquiring ample samples for specific tasks can be challenging due to the high costs associated with data collection or labeling, or the potential risks involved. Therefore, an important research question is how to effectively transfer knowledge from a pre-trained generative model in the source domain (using existing large-scale datasets) to a target domain (for specific tasks) where data is limited.

Training a generative model directly or finetuning a pre-trained generative model on limited data from the target domain often results in significant performance degradation due to overfitting and memorization. To address these issues, numerous studies have proposed methods in generative domain adaptation, including the GAN-based models [46, 45, 49, 1, 51, 28, 48, 9, 15, 43, 22, 50], diffusionbased model [25, 52, 44], etc. Specifically, approaches using diffusion models can be divided into two categories: finetuning lightweight adapters [25, 44] and finetuning with regularization [52]. Approaches involving finetuning lightweight adapters focus on adjusting only a subset of parameters in a pre-trained model. The primary challenge here is identifying which parameters to finetune. This process is typically heuristic and requires preliminary experiments to identify the most efficient parameters for adjustment. Additionally, the specific parameters to be finetuned can vary across

different neural network architectures. On the other hand, the challenge in incorporating regularization during the finetuning process is the heuristic design of the regularization term, which can significantly alter the optimization landscape. We refer to Appendix A for a more detailed discussion of existing literature.

In this work, we introduce a new approach, termed Transfer Guided Diffusion Process (TGDP), to transfer knowledge in the source domain generative model to the target domain with limited samples. Unlike finetuning-based methods that primarily use the pre-trained model as an initialization point, TGDP leverages the pre-trained model as a plug-and-play prior. We show that the score function for the diffusion model on the target domain is the score function on the source domain (which can be pretrained) with additional guidance as shown by Theorem 3.1 and Theorem 3.3. The guidance network is related to the density ratio of the target and source domain data distributions. Consequently, we convert the original optimization problem for a diffusion model on the target domain into estimating the density ratio.

We utilize a domain classifier (binary classifier) along with samples from both domains to efficiently estimate the density ratio. Furthermore, we introduce two additional regularization terms for better training and calibration of the guidance network. These regularization terms are equivalent forms that the optimal guidance network should satisfy, ensuring they do not alter the original optimization problem. We validate the effectiveness of our approach through experiments on Gaussian mixture simulations and real electrocardiogram (ECG) data. Under both fidelity and utility evaluation criteria, TGDP consistently outperforms finetuning-based methods.

Our contributions can be summarized as follows.

We introduce a new framework, the Transfer Guided Diffusion Process (TGDP), for transferring a pre-trained diffusion model from the source domain to the target domain.

We extend TGDP to a conditional version for modeling the joint distribution of data and its corresponding labels, along with two additional regularization terms, which are important for practical applications and downstream tasks.

TGDP demonstrates superior performance over finetuning-based methods on Gaussian mixture simulations and on benchmark electrocardiogram (ECG) data.

The rest of the paper is organized as follows. Section 2 reviews the setup of generative domain adaptation and the diffusion model. Section 3 introduces the proposed method and theoretically characterizes its effectiveness. Numerical results are given in Section 4. We conclude the paper in Section 5. All proofs and additional numerical experiments are deferred to the Appendix.

2 Problem Formulation and Preliminaries

2.1 Transfer Learning Problem Setup

Let X denote the data space and Y the label space. A domain corresponds to a joint distribution over X and Y , denoted as p XY for the source domain and q XY for the target domain. The marginal distribution of data in the source and target domains are p X and q X , respectively. Suppose we have access to m (labeled) samples from the source domain S = { ( x i , y i ) } m i =1 ∼ p XY and n (labeled) samples from the target domain T = { ( x ′ i , y ′ i ) } n i =1 ∼ q XY . Typically, the source domain contains significantly more samples than the target domain, i.e., n ≪ m . This setup reflects the common scenario where there is limited data available for specific tasks in the target domain, while abundant data is readily accessible and stored in the source domain.

The problem of interest is as follows. Given a pre-trained generative model p θ for the data distribution p X in the source domain, and a relatively small number of samples from the target domain, generative domain adaptation approaches aim to obtain a generative model that can generate synthetic samples following the target data distribution q X . We will focus on diffusion generative models, given their great success in synthetic data generation. We first present the key idea of a carefully designed guidance network for the generation of x values only. Then, we extend the method to facilitate conditional generations so that we can generate paired samples with labels, ( x , y ) , and can incorporate downstream classification tasks on the target domain.

2.2 Preliminaries of Diffusion Model

Diffusion models are characterized by their forward and backward processes. For illustrative purposes, we discuss the diffusion model trained on the source domain. The forward process involves perturbing the data distribution p X ( x ) by injecting Gaussian noise, as described by the following continuous-time equation [36]:

where w is the standard Brownian motion, f ( · , t ) : R d → R d is a drift coefficient, and g ( · ) : R → R is a diffusion coefficient. The marginal distribution of x t at time t is denoted as p t ( x t ) , and p 0 is the distribution of the initial value x 0 , which equals the true data distribution p X ( x ) . For notational simplicity and provided it does not cause further confusion, we will refer to this diffusion process as p in the following, and we define p ( x t | x s ) , ∀ s, t , as the conditional distribution of x t given the value x s . Similarly, for initial value x following the target domain distribution, we denote the corresponding probability measure induced by the above diffusion process (1) as q .

Then, we can reverse the forward process (1) for generation, defined as:

where w is a standard Brownian motion when time flows backwards from T to 0, and d t is an infinitesimal negative time step. The key of the backward process is to estimate the score function of each marginal distribution, ∇ x log p t ( x ) , then the generation can be performed by discretizations of (2) [13, 36]. Score Matching [16, 40, 35] are proposed to train a neural network s ϕ ( x t , t ) (parameterized by ϕ ) to estimate the score:

where λ ( t ) : [0 , T ] → R > 0 is a positive weighting function, t is uniformly sampled over [0 , T ] . One commonly adopted forward process is choosing an affine f ( x , t ) = -1 2 β ( t ) x and g ( t ) = √ β ( t ) , which yields the Gaussian transition distribution p ( x t | x s ) = N ( x t ; √ 1 -β ( t ) x s , β ( t ) I ) , t > s , with β ( t ) : [0 , T ] → (0 , 1) as a variance schedule. This is the Variance Preserving Stochastic Differential Equation (VP SDE) that we use in the numerical Section 4.

Several works on image generation [4, 5] and inverse problem [7] extends Score Matching to Conditional Score Matching, i.e.,

where p t ( x t | y ) is the conditional distribution of perturbed data x t given corresponding label y .

3 Transfer Guided Diffusion Process

In this section, we introduce the proposed Transfer Guided Diffusion Process (TGDP) that leverages a pre-trained diffusion model - trained on the source domain data - to generate data in the target domain. The proposed approach is orthogonal to and different from the existing fine-tuning type methods. We introduce the additional guidance in Section 3.1. The methods for calculating the guidance are provided in Section 3.2. We extend our framework to the conditional diffusion model in Section 3.3 and we propose two regularization terms for enhancing the performance of our method in Section 3.4. All proofs are deferred to Appendix C.

3.1 Methodology Formulation

This subsection outlines the process of transferring knowledge from a diffusion generative model pretrained using the source domain data S for generating samples that match the underlying distribution of target domain sample T . The simplest non-transfer type approach involves directly training a diffusion model on samples T from the target domain by denoising Score Matching as described by Eq (3) or Eq (4). However, since we assume only a limited amount of data is accessible on the target domain, directly learning from the target domain is unlikely to yield an effective generative model.

Several studies propose to finetune the pre-trained diffusion model to alleviate the challenges caused by limited data and make use of acquired knowledge [25, 42, 53]. These methods typically design different strategies, such as adapters, to avoid finetuning all weights in a pre-trained model. However, these approaches generally use the pre-trained diffusion model from the source domain only as initial weights. Our method offers a different way for better utilization of the acquired knowledge.

Our proposed method is inspired by the key observation detailed in the following Theorem 3.1. Intuitively, the score function ∇ x t log q t ( x t ) for the target domain differs from the score function ∇ x t log p t ( x t ) of the source domain by a term related to the density ratio function q X /p X . We refer to this differing term as a guidance term in the following Theorem.

Theorem 3.1. Consider two diffusion models on the source and target domain, denoted as p and q , respectively. Let the forward process on the target domain be identical to that on the source domain, q ( x t | x 0 ) = p ( x t | x 0 ) , and s ϕ ∗ ( x t , t ) is the score estimator in the target domain:

then we have

Based on Eq (6), instead of solving s ϕ ∗ from the limited training samples on the target domain, we construct s ϕ ∗ by combing the pre-training score estimator and the guidance based on a binary classifier of source and target domain samples (detailed in Section 3.2). We comment on some potential advantages of this simple yet effective idea. First of all, we do not need to fine-tune the pre-trained diffusion model on the source domain, with the corresponding computation shifted to training the guidance network which is essentially a classifier. Second, the guidance network can be effectively estimated by a domain classifier using data from both the source and target domains. There is also great flexibility in constructing this guidance network due to the extensive literature on classification problems and density ratio estimation approaches. Additionally, the sample complexity for training a generative model could be much larger than a discriminative model, since the generative model needs to recover the full spectrum of target data distribution, while a domain classifier only needs to distinguish whether the sample is from the source or target distribution.

3.2 Learning Guidance Network

We calculate the guidance for the diffusion model on the target domain as defined in the second term of Eq (6) via two steps. In the first step, we estimate the density ratio q ( x 0 ) /p ( x 0 ) by training a classifier c ω ( x ) : X → [0 , 1] to distinguish samples from the source and target domains. We adopt the typical logistic loss as follows:

Then, the density ratio q ( x 0 ) /p ( x 0 ) can be estimated as (1 -c ω ∗ ( x 0 )) /c ω ∗ ( x 0 ) , and it can be shown that the optimal solution to the population counterpart of Eq (7) is exactly the true likelihood ratio [38]. It is worthwhile mentioning that we may only use a subset of source domain samples to learn the classifier c ω to alleviate the unbalanced sample sizes, and we could also adopt modern density ratio estimators to improve the accuracy [31]. After learning the density ratio q ( x 0 ) /p ( x 0 ) , the second step is to calculate the expectation E p ( x 0 | x t ) [ q ( x 0 ) /p ( x 0 )] using Monte Carlo simulation. Since it is hard to sample from q ( x 0 | x t ) , we use the following equivalent formulation to get the value instead. This trick has also been used in previous work such as the Appendix H in [23].

Lemma 3.2. For a neural network h ψ ( x t , t ) parameterized by ψ , define the objective

then its minimizer ψ ∗ = arg min L guidance ( ψ ) satisfies:

ψ

By Lemma 3.2, we estimate the value E p ( x 0 | x t ) [ q ( x 0 ) /p ( x 0 )] using the guidance network h ψ ∗ solved by minimizing the objective function L guidance ( ψ ) , which can be approximated by easy sampling from the joint distribution p ( x 0 , x t ) . Combine the above steps together, the estimated score function for the diffusion generative model on target domain q X can be calculated as follows:

3.3 Extension to the Conditional Version

The approach outlined above is for generating the sample x in the target domain. In this section, we extend the idea to the conditional generation task. Such extension is essential when the label sets in the source and target domain are different since, in such cases, we usually rely on the conditional diffusion model for sampling [18, 21]. We first present the following theorem, which is an analog to Theorem 3.1 within the context of conditional score matching.

Theorem 3.3. Assume x t and y are conditional independent given x 0 in the forward process, i.e., p ( x t | x 0 , y ) = p ( x t | x 0 ) , ∀ t ∈ [0 , T ] , and let the forward process on the target domain be identical to that on the source domain q ( x t | x 0 ) = p ( x t | x 0 ) , and ϕ ∗ is the optimal solution for the conditional diffusion model trained on target domain q ( x 0 , y ) , i.e.,

then

The key difference is we need to estimate the joint density ratio between the source and target domain. We can extend the density ratio estimator in Section 3.2 for estimating joint density ratio, i.e., also feed the label y into the classifier c ω ( x , y ) . The corresponding Lemma and its proof for the conditional version of Lemma 3.2 can be found in Appendix C.3. We further provide a detailed discussion about how to extend this conditional guidance to text-to-image generation tasks and when the source and target domain contain different class labels in Appendix B.

3.4 Additional Regularizations in Practical Implementations

In this subsection, we provide two additional regularization terms in our final objective function, to enhance the performance of the proposed scheme.

Cycle Regularization In the approaches described above, after obtaining the classifier network c ω ∗ , calculation of the additional guidance ∇ x t log E p ( x 0 | x t ) [ q ( x 0 ) /p ( x 0 )] (or ∇ x t log E p ( x 0 | x t ,y ) [ q ( x 0 , y ) /p ( x 0 , y )] for conditional generation) only utilizes the data from source domain. In this section, we provide an enhancement in which the limited data from the target domain can also be utilized to improve the training of the guidance network h ψ .

Notice that (with detailed derivation given in Appendix C.5)

where recall p t ( x t ) and q t ( x t ) are the marginal distribution at time t for source and target distributions, respectively. A similar idea to Theorem 3.2 implies that we can learn the guidance network by solving the following optimization problem as well:

Moreover, in order to estimate the density ratio for marginal distributions at time t between the target and source data distribution, we train a time-dependent classifier c ω ( x , t ) to distinguish samples from

source domain p t ( x ) and target domain q t ( x ) by the logistic loss as follow:

where m,n are the number of training samples in source and target domains. The density ratio q t ( x t ) /p t ( x t ) can then be calculated by (1 -c ω ∗ ( x t , t )) / ( c ω ∗ ( x t , t )) .

Consistency Regularization Motivated by the fact that an optimal guidance network should recover the score in the target domain, we further use score matching in the target domain as the Consistency Regularization L consistence to learn the guidance network better. ψ ∗ = arg min L consistence

Combining these two additional regularization terms together with the original guidance loss (19), the final learning objective for the guidance network can be described as follows:

where η 1 , η 2 ≥ 0 are hyperparameters that control the strength of additional regularization, which also enhances the flexibility of our solution scheme. We summarize the Algorithm of TGDP in Appendix D.1. We provide the ablation studies that demonstrate the effectiveness of these two regularizations in Appendix D.2 and we also empirically show only adopt L consistence to optimize the guidance network is not good enough because of the limited data from the target distribution.

Remark 3.4 (Discussion about related guidance) . Classifier guidance has become a common trick in recent research [36, 8, 3, 6]. We highlight that, under the transfer learning framework, the guidance proposed in our work is the optimal guidance since the resulting score function matches the oracle score on the target domain. On the contrary, vanilla versions of classifier guidance utilizing a domain classifier cannot generate samples that exactly follow target distribution. Indeed, for a pre-trained domain classifier c ω , vanilla domain classifier guidance formulates the source for generation as follows:

̸

4 Experiments

In this section, we present empirical evidence demonstrating the efficacy of the proposed Transfer Guided Diffusion Process (TGDP) on limited data from a target domain. In Section 4.1, we conduct proof-of-concept experiments using a Gaussian mixture model to showcase that the guidance network of TGDP can successfully steer the pre-trained diffusion model toward the target domain. In Section 4.2, we illustrate the effectiveness of TGDP using a real-world electrocardiogram (ECG) dataset.

4.1 Simulation Results

Experimental setup We begin with a Gaussian mixture model where X = R d and Y = {-1 , 1 } . On both domains, the marginal distribution for label y is uniform in Y , and the conditional distribution of features is x | y ∼ N ( y µ , σ 2 I d ) , where µ ∈ R d is non-zero, and I d is the d dimensional identity covariance matrix. We let µ = µ S on the source domain and µ = µ T on the target domain, with ( µ S ) ⊤ µ T = 0 . Under such case, the marginal distribution of x on the source domain p X is a Gaussian mixture, for convenience we denote it as 0 . 5 N ( µ S , σ 2 I ) + 0 . 5 N ( -µ S , σ 2 I ) , and the marginal feature of target distribution q X is 0 . 5 N ( µ T , σ 2 I )+0 . 5 N ( -µ T , σ 2 I ) . We let d = 2 , µ S = [0 . 5 , 0 . 5] , µ T = [0 . 5 , -0 . 5] , σ 2 = 0 . 1 , and draw m = 10000 samples from source domain p X , and n = 10 , 100 , 1000 samples from target domain q X , respectively.

Implementation details and Baselines We adopt the default Variance Preserving (VP) SDE in [36] with a linear schedule, i.e., q ( x t | x 0 ) = p ( x t | x 0 ) = N ( x t | α t x 0 , σ 2 t I ) with α t and σ t being:

with β 0 = 0 . 1 , β 1 = 20 . We adopt 5-layer MLP with hidden sizes of [512 , 512 , 512 , 512 , 256] and SiLU activation function as the diffusion model. We train the diffusion model on data from the source domain for 100 epochs using the Adam optimizer with a learning rate of 1e -4 and batch size of 4096. The guidance network is a 4-layer MLP with 512 hidden units and SiLU activation function. We train the guidance network 20 epochs for our TGDP and train a vanilla diffusion model or finetune the diffusion model target domain 50 epochs. For generation, we adopt DPM-Solver [24] with a second-order sampler and a diffusion step of 25. We compare TGDP with the following baseline methods: 1) Vanilla Diffusion: directly training from target domain; 2) Finetune Diffusion: finetuning all weights of a pre-trained diffusion model on target distribution 2 .

Experimental results We first demonstrate the effectiveness of guidance in Figure 1 under the above setup. Figure 1 (a) plots the source samples, while Figure 1 (b) shows the target samples under different sample sizes n = 10 , 100 , 1000 . Figure 1 (c-e) illustrates the generated target samples via different methods, respectively. It can be seen that the samples generated via the proposed TGDP approach share similar patterns with the target distribution and two mixture components are more obvious as compared with other baseline methods. Furthermore, since the true data distribution of the target domain is known, we calculate the average likelihood of samples generated by each method as demonstrated in Table 1 for quantitative evaluation and comparison.

(b) Target

(a) Source

(c) Vanilla Diffusion

(d) Finetune Diffusion

(e) TGDP

n=10

n=100

n=1000

1.5

1.5

1.0

1.0

1.0

1.0

0.5

0.5

0.5

0.5

0.0

0.0

00

0.0

0.5

-0.5

0.5

1.0

1.0

1.0

-1.0

1.5

1.0

0.5

0.0

0.5

1.0

1

-1.0

-0.5

0.0

0.5

1.0

-121s

-1.0

-0.5

5'0

1.0

1.5

-1.0

-0.5

0.0

0.5

1.0

15

1.5

1.5

1.0

1.0

1.0

1.0

5'0

00

0'0

0'0

0.0

-0.5

-0.5

1.0

1.0

-153

-1.0

0.5

0.0

5'0

1.0

0.3

00

1.0

-0.5

0°0

1.0

1.5

1.5

1.0

1.0

1.0

0.5

0.5

0.0

3.0

3.0

0.0

-0.5

0.5

-1.0

1.0

-0.5

10

1.0

3.0

1.5

1.0

S’0

0.0

0.5

10

1

1.5

1.0

0.5

0.0

0.5

1.0

-1.5

1.5

1.0

0.5

0.0

0.5

1.0

1.5

As a sanity check, we also look at the sensitivity of the learned density ratio estimator (through the classifier network (7)) regarding different sizes of target samples. As shown in Figure 2, even with only 10 samples from the target domain (and 10 samples from the source domain for class balance sampling), we can accurately estimate the landscape of density ratio (although the magnitude of the estimated ratio is not entirely accurate when the number of target samples equal 10).

(a) Oracle

(b) 10 target

(c) 100 target

(d) 1000 target

7.5

5

5

5.0

2.5

0

0.0

2.5

=5

5.0

-10

7.5

-10

10.0

4.2 ECG Data

In this section, we demonstrate the effectiveness of the proposed guidance on the benchmark of electrocardiogram (ECG) data. We first provide the standard synthetic quality and diversity evaluation in Section 4.2.1. Then, we utilize downstream classification tasks to further evaluate the effectiveness of TGDP in Section 4.2.2. We follow the setup of existing benchmarks on biomedical signal processing [37] that regard PTB-XL dataset [41] as the source domain and ICBEB2018 dataset [27] as the target domain. PTB-XL dataset contains 21,837 clinical 12-lead ECG recordings of 10 seconds length from 18,885 unique patients. A 12-lead ECG refers to the 12 different perspectives of the heart's electrical activity that are recorded. Moreover, the PTB-XL dataset is a multi-label dataset with 71 different statements (label). ICBEB2018 dataset [27] comprises 6877 12-lead ECGs lasting between 6 and 60 seconds. Each ECG record is categorized into one of nine classes, which is a subset of labels in the PTB-XL dataset. We randomly select 10% samples as limited target distribution by stratified sampling preserving the overall label distribution in each fold following [41]. We use the data from PTB-XL dataset and ICBEB2018 dataset at a sampling frequency of 100 Hz, which means 100 samples per second. We include more implementation details in Appendix D.3.

4.2.1 Synthetic Quality and Diversity Evaluation

Baseline method We compare TGDP with the following baseline methods to demonstrate the effectiveness of TGDP. 1) Learn a generative model directly (Vanilla Diffusion) : The vanilla way is to learn a generative model directly on limited samples from the target domain. 2) Leveraging the pre-trained generative model from source domain (Finetune Generator ): Since the label set of the target domain is a subset of that in the source domain, a preliminary solution is to utilize the pre-trained diffusion model to generate samples with labels in the target domain.

Experimental results In Table 2, we compare the generation performance on the target domain using two metrics. The first criterion is the widely used Frechet Inception Distance (FID) [12] to evaluate the quality of synthetic data, which calculates the Wasserstein-2 distance between the real data and the synthetic data on the feature space. We use the pre-trained classifier on the target domain as the feature extractor, i.e., xresnet1d50 [37]. The second metric is the coverage [26] that evaluates the diversity of the synthetic data. It is defined as the ratio of real records that have at least one fake (synthetic) record in its sphere. The higher the coverage is, the more diverse the synthetic data are.

From Table 2, we see that TGDP achieves better performance than baseline methods on two criteria, which demonstrates the effectiveness of TGDP on generative transfer learning in scenarios with limited data. Moreover, TGDP has fewer parameters to be trained and less training time. We also demonstrate the T-SNE of the generated ECG data in Figure 3.

4.2.2 TGDP for Downstream Task

In Section 4.2.1, we illustrate that TGDP is capable of generating samples that adhere to the joint distribution of data and labels in the target domain and is diverse enough. In this subsection, we

(a) Vanilla Diffusion

(b) Finetune Generator

(c) TGDP

(d) Real

100

50

75

100

25

75

50

SZ

0

Label 1

Label 3

Label 4

Label 5

Label 6

Label 7

8 (aqe)

-100

25

0S

75

100

25

50

0

Label 0

Label 1

Label 2

Label 3

Label 5

Label 7

Label 4

Label 6

Label 8

-100

100

Label 2

Label 4

Label 5

Label 7

Label 0

Label 1

Label 3

Label 6

Label 8

20

40

-60

08

60

40

0Z

Label 0

Label 1

2 1aqen

(9qe)

Label 5

Label 6

Label 7

Label 4

8 jaqe)

100

50

50

100

100

0C-

50

100

100

-50

50

100

60

40

-20

D

20

40

60

80

further investigate whether utilizing TGDP to acquire a generative model for the target domain yields superior performance compared to existing transfer learning pipelines.

Baseline method First of all, we can utilize the generative model learned in Section 4.2.1 to generate sufficient samples. Incorporated with the original limited sample from the target domain, we can train the classifier, which we still denoted as Vanilla Diffusion , Finetune Generator , and TGDP, respectively. Moreover, we have the following baseline methods. Directly train a classifier on target domain (Vanilla Classifier) : Utilizing the limited data from the target domain, a vanilla classifier can be obtained. Finetune pre-trained classifier (Finetune Classifier) : Instead of training a classifier from scratch on the target domain, the parameters of the classifier trained on the source domain are adjusted by using the limited data from the target domain. To verify the effectiveness of the generative model, we demonstrate that it improves the performance of the learned classifier in the following.

Experimental results We adopt the same evaluation criteria as ECG benchmark [37], i.e., Macroaveraged area under the receiver operating characteristic curve (AUC), Macro-averaged F β -score ( β = 2) , where F β = ( 1+ β 2 ) · TP (1+ β 2 ) · TP + β 2 · FN + FP , and Macro-averaged G β -score with β = 2 , where G β = TP TP + FP + β · FN . In Table 3, TGDP outperforms baseline methods across three evaluation criteria, showcasing its effectiveness in transfer for diffusion model with limited data.

5 Conclusion

In this work, we propose a novel framework, Transfer Guided Diffusion Process (TGDP), for transferring a source-domain diffusion model to the target domain which consists of limited data. Instead of reducing the finetuning parameters or adding regularization for finetuning, TGDP proves the optimal diffusion model on the target domain is the pre-trained diffusion model on the source domain with additional guidance. TGDP outperforms existing methods on Gaussian mixture simulations and electrocardiogram (ECG) data benchmarks.

Limitations and broader impact Overall, this research presents a promising direction for leveraging pre-trained diffusion models to tackle new tasks. The proposed method, TGDP, has potential applications in a wide range of tasks where domain shift exists. A limitation of this study is the lack of empirical validation regarding TGDP's performance on language vision tasks, which we have earmarked for future exploration. Since we propose a generic algorithm for transferring knowledge to new tasks, this technique could enable people to train Deepfakes for disinformation better. Our approach hinges on the efficacy of detection methods in mitigating negative societal consequences.

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A More Discussion on Related Work

Finetune diffusion model on limited data Directly finetuning the pre-trained generative model on limited data from the target domain may suffer from overfitting and diversity degradation. Moon et. al. [25] introduce a time-aware adapter inside the attention block. Since the attention modules take about 10% of parameters in the entire diffusion model, they significantly reduced the turning parameters and alleviated the overfitting. While in [44], the authors only finetune specific parameters related to bias, class embedding, normalization, and scale factor. Zhu et. al. [52] found out the images generated by directly finetuned diffusion models share similar features like facial expressions and lack ample high-frequency details. Therefore, they introduce two regularization terms, pairwise similarity loss for diversity and high-frequency components loss to enhance the high-frequency feature.

The main drawback of finetuning the pre-trained diffusion model is the sample complexity is larger compared with training a classifier since modeling the distribution is a tougher task. In our work, we decompose the diffusion model on the target domain as the diffusion model on the source domain plus a guidance network. Since training a guidance network (essential as a classifier demonstrated in section 3) requires smaller sample complexity, we believe this novel framework might provide a new way for diffusion-based domain adaptation.

Text-to-image diffusion model and learning with human feedback Numerous studies on Text-toImage diffusion models focus on optimizing the diffusion model to align with human preferences and personalize its performance for specific tasks. These endeavors commonly involve strategies such as text-guided zero-shot finetuning [34, 29] or finetuning diffusion model (or its adaptor) through reward-weighted objectives [32, 19, 11, 20, 10]. We acknowledge the significant potential in these approaches, given that language models inherently encapsulate rich semantic information, thereby endowing text-to-image diffusion models with zero-shot transferability. However, it is noteworthy that in domains lacking a substantial amount of paired data for learning semantic mappings, such as biomedical signal processing and electrocardiogram (ECG) data, we refrain from considering these methods as the primary benchmarks in our comparative analysis.

Non-diffusion based approaches in generative domain adaptation Numerous works in generative domain adaptation (or few-shot generative adaptation) study how to improve the transferability of the generative model on limited data from the target domain. Since we mainly focus on the diffusion model, we summarize the primary GAN-based domain adaptation there. They mainly propose to add different kinds of regularization to avoid model collapse [28, 51, 49, 48, 9, 15, 43] or finetune subset of the parameter (adaptor) [1, 45, 22, 50].

B More Discussion on the Potential of the Proposed Method

In this section, we demonstrate the proposed framework is general enough to deal with text-to-image generation tasks and heterogeneous transfer learning.

B.1 Text-to-Image Generation Tasks

Given a source distribution ( x, c t ) ∼ p , where c t denotes text prompts by using the terminology from [47], a pre-trained diffusion model can be trained on the source distribution. Given a target distribution ( x, c t , c f ) ∼ q , where c f denotes a task-specific condition, Zhang et al. [47] can fine-tune the pre-trained model by noise matching objective,

Our method can directly estimate ∇ x t log E p ( x 0 | x t , c t ) [ q ( x 0 , c t , c f ) p ( x 0 , c t ) ] rather than fine-tuning the pretrained diffusion model. Domain classifier c w ( x, y ) can still be used for estimating the density ratio, where y denotes the embedding of the condition. Moreover, directly fine-tuning the diffusion model on data from the target domain used by [47] is similar to the consistency regularization proposed in our work, while they have a more in-depth design for the architecture and have great results on vision-language tasks. However, with limited data from the target distribution, direct fine-tuning may not achieve good enough performance, which is verified in the two-dimensional Gaussian

setting. In [47], Zhang et al. propose to use zero convolution layers, i.e., 1 × 1 convolution layer with both weight and bias initialized to zeros, which alleviates the instability of fine-tuning process. This is very different from our methodology which relies on the smaller sample complexity of the classifier/density ratio estimator.

B.2 Heterogeneous Transfer Learning

̸

When the source and target domain contain different class labels, our framework is still applicable, i.e., when y t = y s ,

To generate an unseen class y t , the key problem here is to choose a particular class from the source domain y s such that we can borrow useful information from the source domain to generate this unseen class from the target domain. The coupling between y t and y s can be learned by solving a static optimal transport problem. More in-depth design, e.g. coupling solved by static optimal transport, can be left to future work.

C Theoretical Details for Section 3

C.1 Proof of Theorem 3.1

Proof. To prove Eq (6), we first build the connection between Score Matching on the target domain and Importance Weighted Denoising Score Matching on the source domain in the following Lemma.

Lemma C.1. Score Matching on the target domain is equivalent to Importance Weighted Denoising Score Matching on the source domain, i.e.,

Proof of Lemma C.1. We first connect Score Matching objective in the target domain to Denoising Score Matching objective in target distribution, which is proven by [40], i.e.,

Then, we split the mean squared error of Denoising Score Matching objective on target distribution into three terms as follows:

where C 1 = E q ( x 0 , x t ) [ ∥∇ x t log q ( x t | x 0 ) ∥ 2 2 ] is a constant independent with ϕ . We can similarly split the objective function in the right-hand side (RHS) of Eq (16) as follows:

where C 2 is a constant independent with ϕ . It is easy to show that the first term in Eq (17) is equal to the first term in Eq (18), i.e.,

where the equality ( i ) is due to q ( x t | x 0 ) = p ( x t | x 0 ) .

Next, we prove the second terms in Eq (17) and Eq (18) are also equivalent:

where the equality ( i ) is again due to q ( x t | x 0 ) = p ( x t | x 0 ) . Thereby we prove Eq 16.

Based on this, we may use Importance Weighted Denoising Score Matching on the source domain to get the analytic form of s ϕ ∗ as follows:

The RHS of Eq (6) can be rewritten as follows:

Since

we can further rewrite the RHS of Eq (6) as follows:

Thereby we complete the proof.

C.2 Proof of Lemma 3.2

Proof. The proof is straightforward and we include it below for completeness. Note that the objective function can be rewritten as

where C is a constant independent of ψ . Thus we have the minimizer ψ ∗ = arg min ψ L guidance ( ψ ) satisfies h ψ ∗ ( x t , t ) = E p ( x 0 | x t ) [ q ( x 0 ) /p ( x 0 )] .

C.3 Conditional version for Lemma 3.2

Lemma C.2. For a neural network h ψ ( x t , y, t ) parameterized by ψ , define the objective

then its minimizer ψ ∗ = arg min ψ L guidance ( ψ ) satisfies:

Proof of Lemma C.2

Proof. The proof is straightforward and we include it below for completeness. Note that the objective function can be rewritten as

where C is a constant independent of ψ . Thus we have the minimizer ψ ∗ = arg min ψ L guidance ( ψ ) satisfies h ψ ∗ ( x t , y, t ) = E p ( x 0 | x t ,y ) [ q ( x 0 , y ) /p ( x 0 , y )] .

C.4 Proof of Theorem 3.3

Proof. The proof is similar to the proof of Theorem 3.1. To prove Eq 11, we first build the connection between the Conditional Score Matching on the target domain and Importance Weighted Conditional Denoising Score Matching on the source domain in the following Lemma:

Lemma C.3. Conditional Score Matching on the target domain is equivalent to Importance Weighted Denoising Score Matching on the source domain, i.e.,

Proof of Lemma C.3. We first connect the Conditional Score Matching objective in the target domain to the Conditional Denoising Score Matching objective in target distribution, which is proven by [4, Theorem 1], i.e.,

Then we split the mean squared error of the Conditional Denoising Score Matching objective on target distribution into three terms as follows:

where C 1 = E q ( x 0 , x t ,y ) [ ∥∇ x t log q ( x t | x 0 ) ∥ 2 2 ] is a constant independent with ϕ , and q ( x t | x 0 , y ) = q ( x t | x 0 ) because of conditional independent of x t and y given x 0 by assumption. We can similarly split the mean squared error of Denoising Score Matching on the source domain into three terms as follows:

where C 2 is a constant independent with ϕ .

It is obvious to show that the first term in Eq (20) is equal to the first term in Eq (21), i.e.,

And the second term is also equivalent:

According to Lemma C.3, the optimal solution satisfies

Then, we use Importance Weighted Conditional Denoising Score Matching on the source domain to get the analytic form of s ϕ ∗ as follows:

Moreover, the RHS of Eq (11) can be rewritten as:

Since

we can further simplify the RHS of Eq (11) as follows:

Thereby, we finish the proof.

C.5 Proof for Cycle Regularization

Proof of Eq (12) .

where p t ( x t ) = ∫ p ( x 0 ) p ( x t | x 0 ) d x 0 and q t ( x t ) = ∫ q ( x 0 ) q ( x t | x 0 ) d x 0 are the marginal distributions at time t of source and target distributions, respectively.

D More Details on Experiments

D.1 Algorithms for TGDP

TGDP adopts Algorithm 1 and 2 for training a domain classifier and Algorithm 3 and 4 for training the guidance network.

Algorithm 1 Training a domain classifier

Require: Samples from the marginal distribution of the source domain p ( x ) and target domain q ( x ) , and initial weights of domain classifier ω .

1: repeat

2: Sample mini-batch data from source distribution and target distribution respectively with batch size b .

3: Take gradient descent step on

4: until converged.

5: return weights of domain classifier ω .

Algorithm 2 Training a time-dependent domain classifier

Require: Samples from the marginal distribution of the source domain p ( x ) and target domain q ( x ) , pre-defined forward transition p ( x t | x 0 ) , and initial weights of domain classifier ω .

1: repeat

2: Sample mini-batch data from source distribution and target distribution respectively with batch size b .

3: Sample time t ∼ Uniform( { 1 , . . . , T } ) and perturb x 0 by forward transition p ( x t | x 0 ) .

4: Take gradient descent step on

5: until converged.

6: return weights of time-dependent domain classifier ω .

Algorithm 3 Training a guidance network (without regularization)

Require: Samples from the marginal distribution of the source domain p ( x ) , pre-defined forward transition p ( x t | x 0 ) , pre-trained domain classifier c ω , and initial weights of guidance network ψ .

1: repeat

2: Sample mini-batch data from source distribution x 0 with batch size b .

3: Sample time t ∼ Uniform( { 1 , . . . , T } ) and perturb x 0 by forward transition p ( x t | x 0 ) .

4: Take gradient descent step on

5: until converged.

6: return weights of guidance network ψ .

Algorithm 4 Training a guidance network (with regularization)

Require: Samples from the marginal distribution of the source domain p ( x ) and target domain q ( x ) , pre-trained diffusion model on source distribution s source ( x t , t ) , pre-defined forward transition q ( x t | x 0 ) , p ( x t | x 0 ) , pre-trained domain classifier c ω ( x 0 ) and time dependent domain classifier c ′ ω ( x 0 , t ) , hyperparameter η 1 , η 2 , and initial weights of guidance network ψ .

1: repeat

2: Sample mini-batch data from source distribution x 0 with batch size b .

3: Perturb x 0 by forward transition p ( x t | x 0 ) .

5: Sample mini-batch data from target distribution x ′ 0 with batch size b .

6: Sample time t ∼ Uniform( { 1 , . . . , T } ) and perturb x ′ 0 by forward transition q ( x ′ t | x ′ 0 ) .

9: Take gradient descent step on

10: until converged.

11: return weights of guidance network ψ .

D.2 Ablation Studies on simulations

In Figure D.2, we demonstrate the ablation studies on simulations. We can see that only using the consistency regularization term (Figure D.2 (b)) is not able to recover the true distribution in the target domain. Our guidance loss together with cycle regularization can learn a good approximation of target distribution while adding consistency regularization can achieve better performance.

D.3 Implementation details for ECG Benchmark

For TGDP and all of the baseline methods, we utilize the same architecture as the conditional generative models for ECG data, SSSM-ECG [2]. For Vanilla Diffusion , we train the diffusion model for 100k iterations by Adam optimizer with a learning rate 2 e -4 . For Finetune Generator , we finetune the pre-trained diffusion model for 50k iterations by Adam optimizer with a learning rate 2 e -5 . For TGDP, we adopt a 4-layer MLP with 512 hidden units and SiLU activation function as the backbone of the guidance network. We train the guidance network for 50k iterations by Adam optimizer with a learning rate 2 e -4 . For utility evaluation, we adopt the same architecture, xresnet1d50 [37], as the backbone. We train the classifier from sketch for 50 epochs with with a learning rate 1e-2. For Finetune Classifier, we finetune a pre-trained classifier for 30 epochs with with a learning rate 1e-3.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a new framework, the Transfer Guided Diffusion Process (TGDP), for transferring a pre-trained diffusion model from the source domain to the target domain. They connect the score function for the target domain and the score function of the source domain with a  guidance term related to the density ratio. They use a classifier to estimate the density ratio and extend TGDP to a conditional version. Besides, Cycle Regularization term and Consistency Regularization term are proposed to improve the performance.\n\nSTRENGTHS:\n1. This paper introduce a novel training paradigm for transferring a pre-trained diffusion model from the source domain to the target domain in a more efficient and effective way. The proposed guidance term proposed in this paper is a technique worthy of reference and further in-depth study by researchers. \n2. The paper is well-written and easy to understand. The theoretical analysis of the robustness is interesting and well described, which helps to understand the proposed techniques.\n3. Experimental results show the effectiveness of the proposed method.\n\nWEAKNESSES:\n1. The part of Extension to the Conditional Version could be more detailed. The authors could discuss what is the Lemma 3.2 in the conditional version.\n2. This paper is missing a comparison with articles related to transfer learning for diffusion models. In experiment part, the authors only compare the TGDP with vanilla diffusion model and finetune generator.\n3. Except Gaussian mixture simulations and benchmark electrocardiogram (ECG) data, the authors could provide more experiment results on other datasets.\n\nQUESTIONS:\n1. Is there a writing mistake in Line.162? It is hard to sample from p(x0|xt) rather than q(x0|xt)?\n2. What is the Lamma 3.2 in the conditional version?\n3. Do you find out other articles related to transfer learning for diffusion models and can you compare other methods with TGDP?\n\nLIMITATIONS:\nA limitation of this study is the lack of empirical validation regarding TGDP’s performance on language vision tasks.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 4, "DATE": "2024-06-25"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses the transfer learning problem for diffusion models, specifically adapting pre-trained diffusion models to downstream datasets, particularly when the data size is small. Traditional parameter-efficient fine-tuning methods often use pre-trained models as parameter initialization, selectively updating parameters based on prior knowledge. These methods, however, can be suboptimal and not robust across different downstream datasets. The authors propose a novel approach called Transfer Guided Diffusion Process (TGDP), which aims to transfer pre-trained diffusion models more effectively. Instead of fine-tuning, TGDP treats the knowledge transfer process as guided by the pre-trained diffusion model. This method involves learning a domain classifier and using its gradient to guide the estimated score function from the source to the target domain, complemented by additional regularizations in practical implementation. Experimental results demonstrate that TGDP outperforms traditional fine-tuning methods, achieving state-of-the-art performance on both synthetic and real-world datasets.\n\nSTRENGTHS:\n1. Provides a novel perspective on knowledge transfer for pre-trained diffusion models.\n2. Theoretical foundation of the proposed method is well-constructed.\n3. The paper is well-organized with clear presentation.\n\nWEAKNESSES:\n1. **Scope of Title:**\n   - The title \"Transfer Learning\" is too broad. The paper focuses solely on (few-shot and supervised) domain adaptation, where the upstream and downstream tasks are similar in nature. General transfer learning encompasses a wider range of tasks, including those with different downstream tasks from the upstream one. For instance, transferring pre-trained text-to-image models to controllable generation or text-to-video generation are broader and more complex tasks that fall under transfer learning.\n   - The paper does not address transfer learning across different label spaces. Even within the same generation tasks, domain adaptation requires identical label spaces for source and target domains, which is not always practical. For example, transferring pre-trained conditional generation models on ImageNet to other fine-grained datasets with different label spaces presents a more challenging problem than the domain adaptation addressed in this paper.\n\n2. **Empirical Results:**\n   - The benchmarks used are insufficient. The authors conduct experiments primarily on synthetic datasets and a single real-world dataset (ETG). This limited scope is inadequate for demonstrating the method's effectiveness. More experiments on various modalities and datasets, such as the DomainNet dataset, which is a benchmark for domain adaptation, are necessary to showcase the generalization ability of the proposed method.\n   - The provided analyses are insufficient. While several ablation studies on simulations are included in Appendix C.2, they are not comprehensive. Essential missing analyses include (1) examining the main term $\\mathcal{L}\\_{\\text{guidance}}$ alone and (2) combining $\\mathcal{L}\\_{\\text{guidance}}$ with $\\mathcal{L}\\_{\\text{cycle}}$. These studies are crucial for understanding each term's effectiveness. Additionally, ablation studies should also be conducted on real-world datasets, not just synthetic ones.\n\nQUESTIONS:\n1. **Consistency Regularization:**\n   - The consistency regularization requires optimization of the gradient term $\\nabla_{x_t}\\log h_\\psi(x_t,t)$, but the paper lacks details on how to optimize this term, especially when second-order gradients are involved. Could the authors elaborate on the optimization process for this term?\n\n2. **Effectiveness of TGDP:**\n   - In Table 1, although TGDP significantly outperforms baselines, its performance is highly dependent on the target data size $n$. This seems contradictory to two points mentioned by the authors: (a) the training of the domain classifier $c$ is not significantly affected by $n$ (Figure 2), and (b) the training of the guidance network $h$ with the main term $\\mathcal{L}_{\\text{guidance}}$ does not require target data (Equation 8). How do the authors explain this discrepancy?\n\n3. **Explanation of Figure 3:**\n   - Figure 3 shows that the visualizations of *Finetune Generator* and *TGDP* appear similar, yet their performance differs significantly. Could the authors provide more insights and explanations about the figure and the reasons behind this performance difference?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2024-07-07"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes an approach for transfer learning based on score-based generative models and density-ratio estimation. The authors show that in order to transfer a trained diffusion model from a source to a target domain, all that is needed is the expectation of density ratios of source and target domains. This expectation can be learned using neural networks reducing the problem of learning a generative model on the target domain to a regression/classification task.\n\nSTRENGTHS:\n- As far as I can judge, the proposed method for transfer learning is both original and significant. It should make a good contribution to the research community.\n- In addition to the core of the method, the proposed regularizers that improve efficiency are in my opinion conceptually convincing.\n- The paper is well written and easy to follow.\n- The experimental evaluation on the ECG data is in my opinion well executed and convincing.\n\nWEAKNESSES:\n- While the method is in my opinion theoretically convincing, the experimental section and ablations are a bit lackluster which decreases confidence in the method (even though I acknowledge the complexity of the task itself). \n- The first experiment on a 2D Gaussian illustrates the performance of the method in comparison to baselines decently, but it is in my opinion ultimately too trivial to be really meaningful (since the density ratios of the 2 Gaussian mixtures can be easily learned, because they are well separated, I would expect that a method based on learning density ratios outperforms baselines here). The ablation in Figure~4 in the appendix is conducted too superficially. It consists of scatterplots, no real quantitative analysis, and doesn't evaluate all relevant loss terms of the model.\n- The evaluation on the ECG data is not fully clear, since meta-information, such as sampling rate, and other details are not given (as far as I can tell).\n- In my opinion, a quantitative evaluation on at least 2-3 more high-dimensional real-world data sets should have been conducted in addition.\n\nQUESTIONS:\n- Figure 1 shows the data as scatterplot which makes it impossible to see the learned density. Since, the true densities are known, a representation using kernel density estimates would be better to see if the learned model aligns with the truth.\n- For readers who do not know what a \"12-lead ECG data\" is, the supplement should contain this information (at least a rough overview). How does 12-lead ECG data look? Are they one-dimensional time series? At what rate are they sampled? \n- Task 4.2.2 is a bit unclear. The authors should be more detailed what the goal is and what they are exactly doing (even though one can infer it from the text).\n- It would have been nice to see the ablation for all combinations that contain $\\mathcal{L}\\_{\\text{guidance}}$, and in particular $\\mathcal{L}\\_{\\text{guidance}}$ alone (and not  $\\mathcal{L}\\_{\\text{consistence}}$). In this state, it is not clear what, e.g.,  $\\mathcal{L}\\_{\\text{cycle}}$ or $\\mathcal{L}\\_{\\text{consistance}}$ contribute separately.\n- How are the hyper-parameter $\\eta$ chosen?\n\nLIMITATIONS:\n- A statement on limitations regarding empirical evaluation exist.\n- Possible negative societal impact, e.g., regarding generation of deepfakes using transfer learning, is acknowledged.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-11"}

comments: SUMMARY:
introduces a novel approach called Transfer Guided Diffusion Process (TGDP) for transferring knowledge from a pre-trained diffusion model in the source domain to a target domain with limited data. The authors present the methodology for transferring knowledge, including the formulation of the guidance network and its learning process. They also extend TGDP to a conditional version for joint data and label distribution modeling.

STRENGTHS:
1. TGDP offers a new perspective on transferring knowledge from pre-trained diffusion models to new domains with limited data. The whole framework is innovative and reasonable.
2. The paper provides a solid theoretical basis for TGDP, including proofs for the optimality of the approach.

WEAKNESSES:
1. More experiments on real-world datasets are required to further validate the effectiveness of the proposed framework.
2. The computational cost of training the guidance network and the diffusion model should be discussed.
3. The paper primarily validates TGDP on Gaussian mixture simulations and ECG datasets. Its performance on other types of data or domains is not empirically tested or discussed.

QUESTIONS:
In what scenarios does the proposed framework work best?

LIMITATIONS:
Authors have discussed limitations well.
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 3
DATE: 2024-07-13