# knowledge_diffusion_for_distillation__02b0912c.pdf

Knowledge Diffusion for Distillation

Tao Huang1,2 Yuan Zhang3 Mingkai Zheng1 Shan You2

Fei Wang4 Chen Qian2 Chang Xu1

1School of Computer Science, Faculty of Engineering, The University of Sydney 2Sense Time Research 3Peking University 4University of Science and Technology of China

The representation gap between teacher and student is an emerging topic in knowledge distillation (KD). To reduce the gap and improve the performance, current methods often resort to complicated training schemes, loss functions, and feature alignments, which are task-specific and feature-specific. In this paper, we state that the essence of these methods is to discard the noisy information and distill the valuable information in the feature, and propose a novel KD method dubbed Diff KD, to explicitly denoise and match features using diffusion models. Our approach is based on the observation that student features typically contain more noises than teacher features due to the smaller capacity of student model. To address this, we propose to denoise student features using a diffusion model trained by teacher features. This allows us to perform better distillation between the refined clean feature and teacher feature. Additionally, we introduce a light-weight diffusion model with a linear autoencoder to reduce the computation cost and an adaptive noise matching module to improve the denoising performance. Extensive experiments demonstrate that Diff KD is effective across various types of features and achieves state-of-theart performance consistently on image classification, object detection, and semantic segmentation tasks. Code is available at https://github.com/hunto/Diff KD.

1 Introduction

The success of deep neural networks is generally accomplished with the requirements of large computation and memory, which restricts their applications on resource-limited devices. One widelyused solution is knowledge distillation (KD) [14], which aims to boost the performance of efficient model (student) by transferring the knowledge of a larger model (teacher).

The key to knowledge distillation lies in how to transfer the knowledge from teacher to student by matching the output features (e.g., representations and logits). Recently, some studies [17, 29] have shown that the discrepancy between student feature and teacher feature can be significantly large due to the capacity gap between the two models. Directly aligning those mismatched features would even disturb the optimization of student and weaken the performance. As a result, the essence of most state-of-the-art KD methods is to shrink this discrepancy and only select the valuable information for distillation. For example, TAKD [29] introduces multiple middle-sized teach assistant models to bridge the gap; SFTN [30] learns a student-friendly teacher by regularizing the teacher training with student; DIST [17] relaxes the exact matching of teacher and student features of Kullback Leibler (KL) divergence loss by proposing a correlation-based loss; Mas KD [18] distills the valuable information in the features and ignores the noisy regions by learning to identify receptive regions that contribute to the task precision. However, these methods need to resort to either complicated training schemes or task-specific priors, making them challenging to apply to various tasks and feature types.

Correspondence to: Shan You <youshan@sensetime.com>.

37th Conference on Neural Information Processing Systems (Neur IPS 2023).

z0 z T zt 1 zt

pθ(zt 1|zt)

Gaussian noise

Image Student feature

Teacher feature

Denoised feature

Student Teacher

Feature Feature

Figure 1: Diffusion model in Diff KD. The diffusion model is trained with teacher feature in diffusion process q (red-dashed arrow), while we feed the student feature to the reverse denoising process pθ (blue arrows) to obtain a denoised feature for distillation. We find that due to capacity limitation, student feature contains more noises and its semantic information is not as salient as the teacher s. Therefore, we treat student feature as a noisy version of teacher feature, and propose to denoise student feature using a diffusion model trained with teacher feature.

In this paper, we proceed from a different perspective and argue that the devil of knowledge distillation is in the noise within the distillation features. Intuitively, we regard the student as a noisy version of the teacher due to its limited capacity or training recipe to learn truly valuable and decent features. However, distilling knowledge with this noise can be detrimental for the student, and may even lead to undesired degradation. Therefore, we propose to eliminate the noisy information within student and distill only the valuable information accordingly. Concretely, inspired by the success of generative tasks, we leverage diffusion models [15, 40], a class of probabilistic generative models that can gradually remove the noise from an image or a feature, to perform the denoising module. An overview of our Diff KD is illustrated in Fig. 1. We empirically show that this simple denoising process can generate a denoised student feature that is very similar to the corresponding teacher feature, ensuring that our distillation can be performed in a more consistent manner.

Nevertheless, directly leveraging diffusion models in knowledge distillation has two major issues. (1) Expensive computation cost. The conventional diffusion models use a UNet-based architecture to predict the noise, and take a large amount of computations to generate high-quality images2. In Diff KD, a lighter diffusion model would suffice since we only need to denoise the student feature. We therefore propose a light-weight diffusion model consisting of two bottleneck blocks in Res Net [11]. Besides, inspired by Latent Diffusion [35], we also adopt a linear autoencoder to compress the teacher feature, which further reduces the computation cost. (2) Inexact noisy level of student feature. The reverse denoising process in diffusion requires to start from a certain initial timestep, but in Diff KD, the student feature is used as the initial noisy feature and we cannot directly get its corresponding noisy level (timestep); therefore, the inexact noisy level would weaken the denoising performance. To solve this problem, we propose an adaptive noise matching module, which measures the noisy level of each student feature adaptively and specifies a corresponding Gaussian noise to the feature to match the correct noisy level in initialization. With these two improvements, our resulting method Diff KD is efficient and effective, and can be easily implemented on various tasks.

It is worth noting that one of the merits of our method Diff KD is feature-agnostic, and the knowledge diffusion can be applied to different types of features including intermediate feature, classification output, and regression output. Extensive experimental results show our Diff KD surpasses current stateof-the-art methods consistently on standard model settings of image classification, object detection, and semantic segmentation tasks. For instance, Diff KD obtains 73.62% accuracy with Mobile Net V1 student and Res Net-50 teacher on Image Net, surpassing DKD [53] by 1.57%; while on semantic segmentation, Diff KD outperforms Mas KD [18] by 1% with PSPNet-R18 student on Cityscapes test set. Moreover, to demonstrate our efficacy in eliminating discrepancy between teacher and student features, we also implement Diff KD on stronger teacher settings that have much more advanced teacher models, and our method significantly outperforms existing methods. For example, with Swin-T student and Swin-L teacher, our Diff KD achieves remarkable 82.5% accuracy on Image Net, improving KD baseline with a large margin of 1%.

2For example, the diffusion model in Stable Diffusion [35] takes 104 GFLOPs on an input resolution of 256 256 [33].

Image Student Denoised student Teacher

Image Student Denoised student Teacher

Figure 2: Visualization of student features, denoised student features and teacher features on COCO dataset. Details and more visualizations can be found in Appendix F.

2 Preliminaries

2.1 Knowledge distillation

Conventional knowledge distillation methods transfer the knowledge of a pretrained and fixed teacher model to a student model by minimizing the discrepancies between teacher and student outputs. Typically, the outputs can be the predictions (e.g., logits in classification task) and intermediate features of model. Given the student outputs F (s) and teacher outputs F (t), the knowledge distillation loss is defined as Lkd := d(F (s), F (t)), (1) where d denotes distance function that measures the discrepancy of two outputs. For example, we can use Kullback Leibler (KL) divergence for probabilistic outputs, and mean square error (MSE) for intermediate features and regression outputs.

2.2 Diffusion models

Diffusion models are a class of probabilistic generative models that progressively add noise to the sample data, and then learn to reverse this process by predicting and removing the noise. Formally, given the sample data z0 RC H W , the forward noise process iteratively adds Gaussian noise to it, i.e., q(zt|z0) := N(zt| αtz0, (1 αt)I), (2) where zt is the transformed noisy data at timestep t {0, 1, ..., T}, αt := Πt s=0αs = Πt s=0(1 βs) is a notation for directly sampling zt at arbitrary timestep with noise variance schedule β [15]. Therefore, we can express zt as a linear combination of z0 and noise variable ϵt:

zt = αtz0 +

1 αtϵt, (3)

where ϵt N(0, I). During training, a neural network Φθ(zt, t) is trained to predict the noise in zt w.r.t. z0 by minimizing the L2 loss between them, i.e.,

Ldiff := ||ϵt Φθ(zt, t)||2 2. (4)

During inference, with the initial noise zt, the data sample z0 is reconstructed with an iterative denoising process using the trained network Φθ:

pθ(zt 1|zt) := N(zt 1; Φθ(zt, t), σ2 t I), (5)

where σ2 t denotes the transition variance in DDIM [40], which accelerates denoising process by sampling with a small number of score function evaluations (NFEs), i.e., z T z T ... z0, where is the sampling interval.

In this paper, we leverage a diffusion model to eliminate the noises in student feature in our knowledge distillation method Diff KD, which will be introduced in the next section.

In this section, we formulate our proposed knowledge distillation method Diff KD. We first convert the feature alignment task in KD to the denoising procedure in diffusion models, this enables us to use diffusion models to match student and teacher outputs for more accurate and effective distillation.

noise prediction

noise feature

+ Time embedding

timestep Student

Conv 1 1 Noise Adapter

latent feature

rec. feature Rec. Loss

denoised student feature

Autoencoder

student feature Z(stu)

Gaussian noise

T noised feature

Noise Adapter Diffusion Model

no gradient

Figure 3: Architecture of Diff KD. Bottleneck denotes the Bottneck block in Res Net [11].

To further improve the computation efficiency, we introduce a feature autoencoder to reduce the dimensions of feature maps, thereby streamlining the diffusion process. Additionally, we propose an adaptive noise matching module to enhance the denoising performance of student feature. The architecture of Diff KD is illustrated in Fig. 3.

3.1 Knowledge diffusion for distillation

Generally, models with different capacities and architectures produce varying preferences on feature representations, even when trained on the same dataset. This discrepancy between teacher and student is crucial to the success of knowledge distillation. Previous studies [19, 21] have investigated the differences between teacher and student features. Kundu et al. [19] observes that the predicted probabilistic distribution of teacher is more sharp and confident than the student s. Similarly, ATS [21] discovers that the variance of wrong class probabilities of teacher is smaller than that of student, indicating that the teacher output is cleaner and more salient. In summary, both studies find that the student has larger values and variances on wrong classes than the teacher, suggesting that the predictions of student contains more noises than the teacher s.

In this paper, we demonstrate that the same trend holds for intermediate features. We visualize the first feature map of FPN in Retina Net [23] on COCO dataset [24] in Fig. 2 and find that the semantic information in teacher feature is much more salient than the student feature. Therefore, we can conclude that both predictions and intermediate features of student model contain more noises than the teacher s, and these noises are difficult to eliminate through simple imitation of the teacher model in KD due to the capacity gap [17]. As a result, a proper solution is to disregard the noises and only imitate the valuable information from both teacher and student. Inspired by the success of eliminating noises in diffusion models [15, 35, 40], we propose to treat the student feature as a noisy version of teacher feature, and train a diffusion model with teacher feature, then use it to denoise the student feature. With the denoised feature that contains only valuable information as teacher feature, we can perform noiseless distillation on them.

Formally, with teacher feature F (tea) and student feature F (stu) used in distillation, we use F (tea) in the forward noise process q(F (tea) t |F (tea)) (Eq. (2)) to train the diffusion model with Ldiff (Eq. (4)). Then the student feature is fed into the iterative denoising process of the learned diffusion model, i.e., pθ(F (stu) t 1 |F (stu) t ) in Eq. (5), where F (stu) is the initial noisy feature of the process. After this denoising process, we obtain a denoised student feature ˆF (stu), which is used to compute the KD loss with the original teacher feature F (tea) in Eq. (1).

3.2 Efficient diffusion model with linear autoencoder

However, we find that the denoising process in Diff KD can be computationally expensive due to the large dimensions of the teacher feature. During training, Diff KD needs to forward the noise prediction network Φθ for T times (we use T = 5 in our method) for denoising the student feature and 1 time for training the noise prediction network with teacher feature. This T + 1 times of forwarding can result in a high computation cost when the dimension of teacher feature is large. To reduce the computation cost of diffusion model, we propose a light diffusion model which is stacked with two bottleneck block in Res Net [11]. Then we follow Latent Diffusion Models [35] and propose to compress the number of channels using a linear autoencoder module. The compressed latent feature is used as the input of diffusion model. As shown in Fig. 3, our linear autoencoder module is composed of two convolutions only, one is the encoder for reducing the number of channels, another one is the decoder

Table 1: Training strategies on image classification tasks. BS: batch size; LR: learning rate; WD: weight decay; LS: label smoothing; EMA: model exponential moving average; RA: Rand Augment [7]; RE: random erasing; CJ: color jitter.

Strategy Dataset Epochs Total BS Initial LR Optimizer WD LS EMA LR scheduler Data augmentation

A1 CIFAR-100 240 64 0.05 SGD 5 10 4 - - 0.1 at 150,180,210 epochs crop + flip

B1 Image Net 100 256 0.1 SGD 1 10 4 - - 0.1 every 30 epochs crop + flip B2 Image Net 450 768 0.048 RMSProp 1 10 5 0.1 0.9999 0.97 every 2.4 epochs {B1} + RA + RE B3 Image Net 300 1024 5e-4 Adam W 5 10 2 0.1 - cosine {B2} + CJ + Mixup + Cut Mix

for reconstruct the teacher features. The output feature of encoder is used to train the diffusion models (Eq. (2)) and supervise the student.

The autoencoder is trained with a reconstruction loss only, which is the mean square error between the original teacher teacher F (tea) and reconstructed teacher feature F (tea) ae , i.e.,

Lae := || F (tea) F (tea)||2 2. (6)

Note that the latent teacher feature Z(tea) used to train diffusion model is detached and has no gradient backward from the diffusion model.

We also use a convolution layer to project the student feature to the same dimension as teacher latent feature Z(tea), denoted as Z(stu). It is then passed to the diffusion model to perform a reverse denoising process (Eq. (5)) and generate the denoised student feature ˆZ(stu). Now we have the latent representation Z(tea) of teacher and the denoised representation of student ˆZ(stu), they are then used to compute the KD loss and supervise the student, i.e.,

Ldiffkd := d( ˆZ(stu), Z(tea)). (7)

Note that our Diff KD is generic and applies to various tasks (e.g., classification, object detection, and semantic segmentaion) and feature types (e.g., intermediate feature, classification output, and regression output). We use simple MSE loss and KL divergence loss as the distance function d to compute the discrepancy of denoised student feature and teacher feature as a baseline implementation of Diff KD, while it is possible to achieve better performance with more advanced distillation losses.

3.3 Adaptive noise matching

As previously discussed, we treat student feature as a noisy version of teacher feature. However, the noisy level, which represents the gap between the teacher and student features, is unknown and may vary depending on different training samples. Therefore, we cannot directly determine which initial timestep we should start the diffusion process. To address this issue, we introduce an adaptive noise matching module to match the noise level of student feature to a pre-defined noise level.

As shown in Fig. 3, we construct a simple convolutional module to learn a weight γ that fuses student output and Gaussian noise, which helps us match the student output to the same noisy level of noisy feature at initial time step T. Therefore, the initial noisy feature in the denoising process becomes

Z(stu) T = γZ(stu) + (1 γ)ϵT . (8)

This noise adaptation can be naturally optimized with the KD loss Lkd, since the optimal denoised student feature that has minimal discrepancy to the teacher feature is obtained when the student feature matches the appropriate noise level in the denoising process.

Overall loss function. The overall loss function of Diff KD is composed of the original task loss, a diffusion loss that optimize the diffusion model, a reconstruction loss to learn the autoencoder, and a KD loss for distillation on teacher features and denoised student features, i.e.,

Ltrain = Ltask + λ1Ldiff + λ2Lae + λ3Ldiffkd, (9)

where λ1, λ2, and λ3 are loss weights to balance the losses. We simply set λ1 = λ2 = 1 in all experiments.

Table 2: Evaluation results of baseline settings on Image Net. We use Res Net-34 and Res Net-50 released by Torchvision [28] as our teacher networks, and follow the standard training strategy (B1). MSE: we implement our baseline for comparisons. : we replace KL divergence loss with more advanced DIST loss in Diff KD.

Student (teacher) Tea. Stu. KD [14] Review [6] DKD [53] DIST [17] MSE Diff KD Diff KD

R18 (R34) Top-1 73.31 69.76 70.66 71.61 71.70 72.07 70.58 72.22 72.49 Top-5 91.42 89.08 89.88 90.51 90.41 90.42 89.95 90.64 90.71

MBV1 (R50) Top-1 76.16 70.13 70.68 72.56 72.05 73.24 72.39 73.62 73.78 Top-5 92.86 89.49 90.30 91.00 91.05 91.12 90.74 91.34 91.48

Table 3: Performance of students trained with strong strategies on Image Net. The Swin-T is trained with strategy B3 in Table 1, others are trained with B2. The Res Net-50 is trained by TIMM [44], and Swin-L is pretrained on Image Net-22K.

Teacher Student Top-1 ACC (%) Tea. Stu. KD [14] RKD [31] SRRL [47] DIST [17] Diff KD

Res Net-50 Res Net-34

80.1 76.8 77.2 76.6 76.7 77.8 78.1 Mobile Net V2 73.6 71.7 73.1 69.2 74.4 74.9 Efficient Net-B0 78.0 77.4 77.5 77.3 78.6 78.8

Swin-L Res Net-50 86.3 78.5 80.0 78.9 78.6 80.2 80.5 Swin-T 81.3 81.5 81.2 81.5 82.3 82.5

4 Experiments

In this paper, to sufficiently validate the generalization of our Diff KD, we conduct extensive experiments on image classification, object detection, and semantic segmentation tasks.

4.1 Image Net classification

Settings. Following DIST [17], we conduct experiments on baseline settings and stronger teacher settings. The training strategies for CIFAR-100 and Image Net datasets are summarized in Tab. 1. On baseline settings, we use Res Net-18 [11] and Mobile Net V1 [16] as student models, and Res Net-34 and Res Net-50 as teachers, respectively; and the training strategy (B1) is the most common one in previous methods [6, 17, 53]. While for the stronger teacher settings, we train students with much stronger teacher models (Res Net-50 and Swin-L [26]) and strategies (B2 and B3).

We implement our Diff KD on the output feature of backbone before average pooling, and the output logits of classification head, and the distance functions are MSE and KL divergence (with a temperature factor of 1), respectively. We set λ1 = λ2 = λ3 = 1.

Results on baseline settings. We summarized the results on baseline settings in Tab. 2. Our methods outperforms existing KD methods with a large margin, especially on the Mobile Net and Res Net50 setting, Diff KD significantly surpasses previous state-of-the-art DIST [17] by 0.38% on top-1 accuracy. For comparisons with our baseline one feature distillation, we also report the MSE results with the same distillation location as Diff KD. We can see that, by only adding our diffusion model for feature alignment, Diff KD obviously improves the MSE results by 1.74% on Res Net-18 and 1.23% on Mobile Net V1. Moreover, we replace the KL divergence loss in the output logits of Diff KD with the advanced loss function DIST, which achieves further improvements. For instance, Diff KD with DIST loss improves DIST by 0.42% on Res Net-18. This indicates that our feature alignment in Diff KD is generic to different KD losses and can be further improved by changing the losses.

Results on stronger teacher settings. To fully investigate the efficacy of Diff KD on reducing the distillation gap between teacher feature and student feature, we further conduct experiments on much stronger teachers and training strategies following DIST. From the results summarized in Tab. 3, we can see that Diff KD outperforms DIST on all model settings, especially for the most light-weight Mobile Net V2 in the table, Diff KD surpasses DIST by 0.5%. It is worth to remind that our Diff KD only uses the simple KL divergence loss and MSE loss on the stronger settings, the performance could be further improved if we use more advanced loss functions such as DKD [53] and DIST [17].

Table 4: Object detection performance with baseline settings on COCO val set. T: teacher. S: student. : we replace MSE with an attentionbased MSE loss.

Method AP AP50 AP75 APS APM APL Two-stage detectors

T: Faster RCNN-R101 39.8 60.1 43.3 22.5 43.6 52.8

S: Faster RCNN-R50 38.4 59.0 42.0 21.5 42.1 50.3 Fitnet [36] 38.9 59.5 42.4 21.9 42.2 51.6 FRS [9] 39.5 60.1 43.3 22.3 43.6 51.7 FGD [48] 40.4 - - 22.8 44.5 53.5 Diff KD 40.6 60.9 43.9 23.0 44.5 54.0 Diff KD 40.7 61.0 44.3 22.6 44.6 53.7 One-stage detectors T: Retina Net-R101 38.9 58.0 41.5 21.0 42.8 52.4 S: Retina Net-R50 37.4 56.7 39.6 20.0 40.7 49.7 Fitnet [36] 37.4 57.1 40.0 20.8 40.8 50.9 FRS [9] 39.3 58.8 42.0 21.5 43.3 52.6 FGD [48] 39.6 - - 22.9 43.7 53.6 Diff KD 39.7 58.6 42.1 21.6 43.8 53.3 Diff KD 39.8 58.7 42.5 21.5 43.6 53.2 Anchor-free detectors T: FCOS-R101 40.8 60.0 44.0 24.2 44.3 52.4 S: FCOS-R50 38.5 57.7 41.0 21.9 42.8 48.6 FRS [9] 40.9 60.3 43.6 25.7 45.2 51.2 FGD [48] 42.1 - - 27.0 46.0 54.6 Diff KD 42.4 61.0 45.8 26.6 45.9 54.8 Diff KD 42.5 61.1 45.6 25.2 46.8 55.1

Table 5: Object detection performance with stronger teachers on COCO val set. CM RCNN: Cascade Mask RCNN. : we replace MSE with an attention-based MSE loss.

Method AP AP50 AP75 APS APM APL Two-stage detectors

T: CM RCNN-X101 45.6 64.1 49.7 26.2 49.6 60.0

S: Faster RCNN-R50 38.4 59.0 42.0 21.5 42.1 50.3 COFD [13] 38.9 60.1 42.6 21.8 42.7 50.7 FKD [50] 41.5 62.2 45.1 23.5 45.0 55.3 FGD [48] 42.0 - - 23.7 46.4 55.5 Diff KD 42.2 62.8 46.0 24.2 46.6 55.3 Diff KD 42.4 62.9 46.4 24.0 46.7 55.2 One-stage detectors T: Retina Net-X101 41.2 62.1 45.1 24.0 45.5 53.5 S: Retina Net-R50 37.4 56.7 39.6 20.0 40.7 49.7 COFD [13] 37.8 58.3 41.1 21.6 41.2 48.3 FKD [50] 39.6 58.8 42.1 22.7 43.3 52.5 FGD [48] 40.4 - - 23.4 44.7 54.1 Diff KD 40.7 60.0 43.2 22.2 45.0 55.2 Diff KD 41.4 60.7 44.0 23.0 45.4 55.8 Anchor-free detectors T: Rep Points-X101 44.2 65.5 47.8 26.2 48.4 58.5 S: Rep Points-R50 38.6 59.6 41.6 22.5 42.2 50.4 FKD [50] 40.6 61.7 43.8 23.4 44.6 53.0 FGD [48] 41.3 - - 24.5 45.2 54.0 Diff KD 41.7 62.6 44.9 23.6 45.4 55.9 Diff KD 41.9 62.8 45.0 24.4 45.7 55.3

Results for CIFAR-100 dataset are summarized in Appendix C.

4.2 Object detection

Settings. Following FGD [48], we conduct experiments on baseline settings and stronger teacher settings. On baseline settings, we adopt various network architectures, including two-stage detector Faster-RCNN [34], one-stage detector Retina Net [23], and anchor-free detector FCOS [42], and use Res Net-50 [11] as student models, and Res Net-101 as teachers, respectively. The training strategy is the most common one in previous methods [9, 18, 48]. While for the stronger teacher settings, we train students with much stronger teacher models, including two-stage detector Cascade Mask RCNN [2], one-stage detector Retina Net [23], and anchor-free detector Rep Points [49], and stronger backbone Res Ne Xt-101 (X101) [45].

We conduct feature distillation on the predicted feature maps, and train the student with our Diff KD loss Ldiffkd, regression KD loss, and task loss. Note that we do not use linear autoencoder in Diff KD since the number of channels in FPN is only 256. We set λ1 = λ2 = 1. Besides using MSE loss in feature distillation, we also adopted a simple attention-based MSE loss (marked with in Tab. 4) inspired by FGD [48] to balance the foreground and background distillations, which is acknowledged important for detection KD [10, 18, 48]. Details can be found in Appendix B.

Results on baseline settings. Our results compared with previous methods are summarized in Table 4. Our Diff KD can significantly improve the performance of student models over their teachers on various network architectures. For instance, Diff KD improve FCOS-R50 by 4.0 AP and surpasses FGD [48] by 0.4 AP. Besides, the attention-based MSE loss affords consistent improvements on vanilla Diff KD by 0.1 AP.

Results on stronger teacher settings. We further investigate our efficacy on stronger teachers whose backbones are replaced by stronger Res Ne Xts [45]. As in Table 5, student detectors achieve

Table 6: Semantic segmentation results on Cityscapes dataset. : trained from scratch. Other models are pretrained on Image Net. FLOPs is measured based on an input size of 1024 2048.

Method Params FLOPs m Io U (%) (M) (G) Val Test

T: Deep Lab V3-R101 61.1 2371.7 78.07 77.46

S: Deep Lab V3-R18 13.6 572.0 74.21 73.45 CWD [38] 13.6 572.0 75.55 74.07 CIRKD [46] 13.6 572.0 76.38 75.05 Mas KD [18] 13.6 572.0 77.00 75.59 Diff KD 13.6 572.0 77.78 76.24

S: Deep Lab V3-R18 13.6 572.0 65.17 65.47 CWD [38] 13.6 572.0 67.74 67.35 CIRKD [46] 13.6 572.0 68.18 68.22 Mas KD [18] 13.6 572.0 73.95 73.74 Diff KD 13.6 572.0 74.45 74.52

Method Params FLOPs m Io U (%) (M) (G) Val Test

T: Deep Lab V3-R101 61.1 2371.7 78.07 77.46

S: PSPNet-R18 12.9 507.4 72.55 72.29 CWD [38] 12.9 507.4 74.36 73.57 CIRKD [46] 12.9 507.4 74.73 74.05 Mas KD [18] 12.9 507.4 75.34 74.61 Diff KD 12.9 507.4 75.83 75.61

S: Deep Lab V3-MBV2 3.2 128.9 73.12 72.36 CWD [38] 3.2 128.9 74.66 73.25 CIRKD [46] 3.2 128.9 75.42 74.03 Mas KD [18] 3.2 128.9 75.26 74.23 Diff KD 3.2 128.9 75.71 74.96

more enhancements with our Diff KD, especially when with a Retina-X101 teacher, Diff KD gains a substantial improvement of 4.0 AP over the Retina-R50. Additionally, our methods outperforms existing KD methods with a large margin, and significantly surpasses FGD [48] when distilling on Retina Net and Rep Points, by 1.0 and 0.6 AP, respectively. Moreover, comparing Table 4 with 5, we can infer that when the teacher is stronger, the benefit of Diff KD is more significant, as the discrepancy between the student and a stronger teacher is larger.

4.3 Semantic segmentation

Settings. Following CIRKD [46], we use Deep Lab V3 [5] framework with Res Net-101 (R101) [11] backbone as the teacher network. While for the students, we use various frameworks (Deep Lab V3 and PSPNet [54]) and backbones (Res Net-18 [11] and Mobile Net V2 [37]) to valid our efficacy.

We conduct feature distillation on the predicted segmentation maps, and train the student with our Diff KD loss and task loss, as formulated in Eq. (9). Note that we do not use linear autoencoder in Diff KD since the number of channels in segmentation map is only 19. Detailed training strategies are summarized in Appendix B.

Results. The experimental results are summarized in Tab. 6. Our Diff KD significantly outperforms the state-of-the-art Mas KD on all settings. For example, on Deep Lab V3-R18 student, Diff KD improves Mas KD by 0.78% on val set and 0.65 on test set.

4.4 Ablation study

Table 7: Comparisons of different distillation features in Diff KD.

Method Top-1 (%)

w/o KD 70.13 MSE 72.39 KL div. 70.68 Diff KD (feature) 73.16 Diff KD (logits) 72.89 Diff KD (feature + logits) 73.62

Effects of adopting Diff KD on different types of features. On image classification, we distill both intermediate feature (the output feature of backbone before average pooling) and output logits with Diff KD. Here we conduct experiments to compare the effects of distillations on different features of Mobile Net V1 student and Res Net-50 teacher in Tab. 7. We can see that, by adopting Diff KD to align the student features, both feature-level Diff KD and logits-level Diff KD can obtain obvious improvements without changing the loss functions. Meanwhile, combining feature and logits distillations together in our final method achieves the optimal 73.62% top-1 accuracy.

Effects of linear autoencoder. We compare different dimensions of linear autoencoder in Tab. 8. We can see that, the linear autoencoder can significantly reduces the FLOPs of diffusion model, but if we

Table 8: Comparisons of different dimensions of linear autoencoder in Diff KD. We report the top-1 accuracy and FLOPs of diffusion models with Mobile Net V1 student and Res Net-50 teacher on Image Net.

w/o AE 128 256 512 1024 2048

Top-1 (%) 73.47 72.84 73.22 73.53 73.62 73.58 FLOPs (G) 1.41 0.04 0.09 0.21 0.58 1.82

conduct high compression ratios like 128 and 256 dimensions, the distillation performance will be severely weakened. Interestingly, AE with 512, 1024, and 2048 dimensions can outperform the one without AE, a possible reason is that the AE encodes common and valuable information in the original feature for reconstruction and would have better feature representations than the original feature. As a result, we use AE with 1024 dimension in our experiments for better performance-efficiency trade-off.

Effects of adaptive noise matching. We propose adaptive noise matching (ANM) to match the noisy level of student feature to the correct initial level in the denoising process. Here we conduct experiments to validate its efficacy. We train Mobile Net V1 student with the only removal of ANM in our final method, and the Diff KD without ANM obtains 73.34% top-1 accuracy, which has a decrease of 0.28 on our Diff KD with ANM. This indicates that ANM can improve the performance by generating better denoised student feature.

1 3 5 10 20

Figure 4: Results of Diff KD with different NFEs. We use Mobile Net V1 student and Res Net-50 teacher on Image Net.

Ablation on numbers of score function evaluations (NFEs). In diffusion models, the number of score function evaluations (NFEs) is a important factor for controlling the generation quality and efficiency. The early method such as DDPM [15] requires to run a complete timesteps in the reverse denoising process as training, which leads to a heavy computational budget. Recently, some works [27, 40] have been proposed to accelerate the denoising process by sampling a small number of timesteps. In this paper, we use DDIM [40] for speedup. Here, we conduct experiments to show the influence of different NFEs. As shown in Fig. 4, compared to the 72.39% accuracy of MSE baseline without denoising on student feature, only one-step denoising also achieves a significant improvement. However, its performance is weaker than that of those larger NFEs due to the limitation of denoising quality. A NFEs of 5 would suffice in our KD setting to achieve promising performance, and we use it in all experiments for a better efficiency-accuracy trade-off.

5 Conclusion

In this paper, we investigate the discrepancy between teacher and student in knowledge distillation. To reduce the discrepancy and improve the distillation performance, we proceed from a new perspective and propose to explicitly eliminate the noises in student feature with a diffusion model. Based on this idea, we further introduce a light-weight diffusion model with a linear autoencoder to reduce the computation cost of our method, and an adaptive noise matching module to align the student feature with the correct noisy level, thus improving the denoising performance. Extensive experiments on image classification, object detection, and semantic segmentation tasks validate our efficacy and generalization.

Acknowledgements

This work was supported in part by the Australian Research Council under Projects DP210101859 and FT230100549.

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A Related Work

A.1 Representation gap in knowledge distillation

An emerging topic in knowledge distillation is the representation gap between teacher and student. Recently, the models have been designed larger and more complicated, with remarkable performance improvements compared to the traditional models. As a result, an intuitive idea to improve efficient models is to distill them from a stronger teacher model. However, recent studies [29, 39] find that KD performance with a stronger teacher is poor and even worse than the normal teacher. TAKD [29] states that the student can only learn the knowledge effectively from a teacher model up to a fixed capacity, and proposes training multiple teaching assistants that have moderate capacities compared to the narrow student and a huge teacher. The teach assistants are trained sequentially with their former larger teach assistants, and the final smallest teach assistant is used to train the student. DAKD [39] further improves TAKD by densely connecting all models (teacher, assistant teachers, and student) together and letting the student choose the optimal teacher for each sample. SFTN [30] proposes to learn the teacher model with the supervision of student model, which obtains a student-friendly teacher with smaller representation gap to the student. However, such methods suffer from complex distillation algorithms and heavy computational cost for training the teacher model, therefore, they are not applicable in practice. More recently, DIST [17] proposes an efficient and simple approach, which aims at relaxing the exact matching in previous KL divergence loss with a correlation-based loss, which performs better when the discrepancy between teacher and student is large. However, such heuristic loss in DIST only adapts to classification outputs, and thus for dense prediction tasks such as object detection, which requires detailed semantic information in intermediate features, the efficacy is limited. Moreover, the Pearson correlation in DIST only has shift and scale invariances, whereas for the complex situation of dicrepancy in features, it cannot ignore all noises for a clean distillation.

As a result, we present Diff KD, which adapts well to multiple types of features and tasks, and handles better in eliminating the discrepancy in distillation features.

A.2 KD in dense prediction tasks

Different from the image classification task that only needs to recognize the overall classification of the image, object detection and semantic segmentation are referred as dense prediction tasks that have to predict the bounding boxes and classes for all the objects inside the image, or the pixel-level segments of image. As a result, effectively distilling the knowledge of the teacher in these tasks is more challenging than classification.

Various methods [3, 10, 20, 38, 48, 51] are proposed to improve KD performance in object detection. Chen et al. [3] first proposes performing KD on the classification logits and regressions of the Ro I head. Mimicking [20] states that the feature maps in detection model contains richer semantic information than the responses, and proposes to distill the FPN [22] features of teacher. However, distilling from the features suffers from severe imbalance of the foreground and background pixels in object detection. To address this issue, recent methods focus on selecting valuable features and propose various loss functions based on this [10, 18, 38, 48, 52].

In semantic segmentation, knowledge distillation techniques typically prioritize maintaining the structural semantic connections between the teacher and student models. To address the inconsistency between teacher and student features, He et al. [12] employ a pretrained autoencoder to optimize feature similarity in a transferred latent space. They also transfer non-local pairwise affinity maps to minimize feature discrepancies. SKD [25] conducts pairwise distillation among pixels to preserve pixel relationships and adversarial distillation on score maps to distill holistic knowledge. IFVD [43] transfers intra-class feature variation from teacher to student to establish more robust relations with class-wise prototypes. CWD [38] proposes channel-wise distillation to better mimic spatial scores along the channel dimension. CIRKD [46] proposes intra-image and cross-image relational distillations to learn better semantic relations from the teacher.

However, existing state-of-the-art KD approaches in dense prediction tasks are designed specifically for the tasks, which are difficult to be applied to various tasks, resulting in a large experiment cost in evaluating and adapting those methods. As a result, an interesting direction in KD is to generalize and unify KD methods in different tasks.

B Implementation Details

B.1 Diffusion model

In all experiments, we use DDIM [40] as the noise scheduler in reverse denoising process. The total range of timesteps for training is 1000, and the initial time step for denoising is 500.

B.2 Image classification

On Image Net classification task, we simply set λ1 = λ2 = λ3 = 1 in all experiments. (1) Feature distillation. For experiments that use Res Net-50 or Res Net-34 as the teacher model, we set the number of latent channels in our autoencoder to 1024; while for Swin-L teacher, its feature for distillation has 1536 channels, so we compress it to 768 with autoencoder. (2) Logits distillation. We also add a Diff KD loss on the predicted classification logits. Different from the Bottleneck block used in feature distillation, we use MLP (two linear layers associated with an activation function) as an alternate of Bottleneck since the logits have only two dimensions (no spatial dimensions). Besides, the autoencoder is not used in logits distillation. On CIFAR-100 dataset, we also implement Diff KD on the output feature before average pooling layer and classification logits, but remove the autoencoder since the computation cost on CIFAR model is small.

B.3 Object detection

For object detection task, we conduct feature distillation on the predicted feature maps, and train the student with our Diff KD loss Ldiffkd, regression KD loss, and task loss. Note that we do not use linear autoencoder in Diff KD since the number of channels in FPN is only 256. We set λ1 = λ3 = 1. We adopt Image Net pre-trained backbones during training following previous KD works [18]. All the models are trained with the official strategies (SGD, weight decay of 1e-4) of 2 schedule in MMDetection [4]. We run all the models on 8 V100 GPUs.

Loss weights: We set Diff KD loss weight to 5 and regression loss weight to 1 on Faster RCNN students. For other detection frameworks, we simply adjust the loss weight of Diff KD to keep a similar amount of loss value as Faster RCNN. Concretely, the loss weights of LDiff KD on Retina Net, FCOS, and Rep Points are 5, 5, and 15, respectively.

B.4 Semantic segmentation

Following CIRKD [46] and Mas KD [18], we train the models with standard data augmentations including random flipping, random scaling in the range of [0.5, 2], and a crop with size 512 1024. An SGD optimizer with momentum 0.9 is adopted, and the learning rate is annealed using a polynomial scheduler with an initial value of 0.02. For Diff KD, we distill the knowledge of the segmentation predictions of teacher. Since these predictions are probabilistic distributions, we use DIST [17] as the distance function d in KD loss. We do not involve autoencoder since the segmentation prediction has only 19 channels on Cityscapes dataset, and set λ1 = λ3 = 1.

C More Experiments

C.1 Results on CIFAR-100 dataset

We summarize the CIFAR-100 results in Tab. 9. Our Diff KD surpasses previous methods in most cases. Moreover, comparing homogeneous architecture settings and heterogeneous architecture settings, Diff KD gains more significant improvements on heterogeneous settings compared to the standalone training results, which indicates that our method can deal better with the discrepancy between teacher and student models.

C.2 Effect of efficient diffusion model

We train Retina Net R50 student with R101 teacher with 1 schedule in COCO, and compare our Effieicnt DM with original UNet in DDPM using Diff KD. As shown in Tab. 10, with feature shape (256, 80, 124), the original UNet has much larger parameters and GFLOPs, and thus leads to 3

Table 9: Evaluation results on CIFAR-100 dataset. The upper and lower models denote teacher and student, respectively.

Homogeneous architecture style Heterogeneous architecture style

WRN-40-2 WRN-40-1 Res Net-56 Res Net-20 Res Net-32x4 Res Net-8x4

Res Net-50 Mobile Net V2 Res Net-32x4 Shuffle Net V1 Res Net-32x4 Shuffle Net V2

Teacher 75.61 72.34 79.42 79.34 79.42 79.42 Student 71.98 69.06 72.50 64.6 70.5 71.82 Fit Net [36] 72.24 0.24 69.21 0.36 73.50 0.28 63.16 0.47 73.59 0.15 73.54 0.22 VID [1] 73.30 0.13 70.38 0.14 73.09 0.21 67.57 0.28 73.38 0.09 73.40 0.17 RKD [31] 72.22 0.20 69.61 0.06 71.90 0.11 64.43 0.42 72.28 0.39 73.21 0.28 PKT [32] 73.45 0.19 70.34 0.04 73.64 0.18 66.52 0.33 74.10 0.25 74.69 0.34 CRD [41] 74.14 0.22 71.16 0.17 75.51 0.18 69.11 0.28 75.11 0.32 75.65 0.10 KD [14] 73.54 0.20 70.66 0.24 73.33 0.25 67.35 0.32 74.07 0.19 74.45 0.27 DIST [17] 74.73 0.24 71.75 0.30 76.31 0.19 68.66 0.23 76.34 0.18 77.35 0.25 Diff KD 74.09 0.09 71.92 0.14 76.72 0.15 69.21 0.27 76.57 0.13 77.52 0.21

Table 10: Comparisons of different dimensions of linear autoencoder in Diff KD. We report the top-1 accuracy and FLOPs of diffusion models with Mobile Net V1 student and Res Net-50 teacher on Image Net.

w/o AE 128 256 512 1024 2048

Top-1 (%) 73.47 72.84 73.22 73.53 73.62 73.58 FLOPs (G) 1.41 0.04 0.09 0.21 0.58 1.82

training time. The original UNet only achieves similar performance as our Efficient DM, as the generation of features is easier than images, and a small model would suffice.

C.3 Effect of adaptive noise matching (ANM)

To validate the efficacy of ANM more thoroughly, we conducted further experiments in more model settings and training strategies, as summarized in Tab. 11. We can see that, when with stronger strategy and teacher, the improvement of ANM is more significant (1.2% improvement on Mobile Net V2 compared to 0.3% and 0.5% improvements on Mobile Net V1 and Res Net-18). One possible reason is that, when the augmentations and teacher become stronger, the noisy gaps between predicted features of teacher and student become more various, and therefore ANM is more effective in matching the noisy levels.

C.4 Statistics of the learned noise weight γ

To analyze the effectiveness of ANM, we first show the distribution of noise weight γ in Fig. 5 (a) of the rebuttal PDF. Revealing that the student feature is noised with Z(stu) T = γZ(stu) + (1 γ)ϵT , the larger γ denotes smaller additional noise added.

We can see that a large amount of values is in the range of γ > 0.9, indicating that the student feature itself contains nonnegligible noises and only requires small noises to match the initial noise level, while there also exist some cleaner samples that require large noises.

We also plot the curves of average γ in each epoch during training. Fig. 5 (b) indicates that, at the beginning of training, the student feature contains more noises, so only small weights of noises should be added. When the model gets converged, the noise in student feature becomes smaller and γ goes smaller to match the noise level accordingly.

Table 11: Effects of adaptive noise matching (ANM) on various model settings.

Student Teacher Strategy w/ ANM w/o ANM

Mobile Net V1 Res Net-50 B1 73.6 73.3 Res Net-18 Res Net-34 B1 72.2 71.7 Mobile Net V2 Res Net-50-SB B2 74.9 73.7

Percentile (%)

γ 0.5 0.6 0.7 0.8 0.9 1.0

Epoch 0 20 40 60 80 100

Figure 5: Statistics of learned noise weight γ on Mobile Net V1 student. (a) Histogram of learned γ during training. (b) curves of average γ in each epoch during training.

C.5 Effects of different feature types of distillations on object detection

We conduct experiments on COCO dataset to compare the effects of performing distillations on FPN features, classification outputs, and regression outputs. As the results shown in Tab. 12, compared with the original KD without feature denoise in Diff KD, our method obtains significant improvements on all the feature types. Besides, comparing these features, distillation on FPN feature obtains relative high performance, which demonstrates that the semantic information in intermediate features is more valuable than the responses. We also conduct experiment to combine all the feature distillations in Diff KD together, while it achieves similar performance of FPN feature, this infers that the distillation on FPN feature is sufficient to obtain a good performance.

Table 12: Comparison of original diffusion model (DM) and our efficient DM on COCO dataset.

DM Params GFLOPs Training time AP AP AP

UNet (DDPM) 13.62 M 650.77 1.80 8 GPU Days 39.1 58.0 41.9 Efficient DM (ours) 0.21 M 132.76 0.59 8 GPU Days 39.2 58.1 42.0

C.6 Efficiency analysis

In Diff KD, we use a light-weight diffusion model to denoise the student feature. Here we analyze the computation efficiency with comparisons to other methods. Compared to the vanilla KD, Diff KD has additional computations to denoise the intermediate feature and output logits on Image Net. Specifically, for Res Net-18 student and Res Net-34 teacher, the additional FLOPs is 800M. However, compared to other feature-based KD methods, the cost is acceptable. For example, CRD [41] uses extra 260M FLOPs, Review KD has an addtional computation cost of 1900M.

D Discussion

D.1 Limitation

In this paper, we only implement our diffusion model with simple convolutions and DDIM inference algorithm, while there exists recent advances of diffusion models that propose better transformerbased models and more efficient inference algorithm. Besides, we only use the traditional mean square error and KL divergence as our KD loss functions, while many novel losses could be leveraged

to further improve the distillation performance. The computational cost is larger than the simple logits distillation methods such as KD [14] and DIST [17], but the cost is comparable to existing feature distillation methods and does not affect the computation cost in inference.

D.2 Societal impacts

Investigating the efficacy of the proposed method would consume considerable computing resources. These efforts can contribute to increased carbon emissions, which could raise environmental concerns. However, the proposed knowledge distillation method can improve the performance of light-weight compact models, where replacing the heavy models with light models in production could save more energy consumption, and it is necessary to validate the efficacy of Diff KD adequately.

E Visualization of Predicted Classification Scores

We visualize the predicted classification scores in Fig. 6. The original predictions of student, have different sharpness compared to the teacher s, while the denoised predictions align better to the predictions of teacher.

Shetland sheepdog

Figure 6: Visualization of predicted scores of Mobile Net V1 student on Image Net validation set. Diff KD has an effect of matching the sharpness of the probabilistic distributions of teacher and student.

F Visualization of Features

F.1 Visualization details

We visualize the features of student and teacher models in the first output (stride 4) of FPN. The models used to extract the feature are Retina Net-R50 (student) and Retina Net-X101 (teacher) trained on COCO dataset. Following FGD [48], we average the feature map along channel axis and perform softmax on the spatial axis to measure the saliency of each pixel. Formally, with a given feature map X RC HW , we first average the channels and get X RHW , where X i = 1 HW PHW i=1 (X:,i). Then we generate the attention map for visualization as V = H W softmax(X /τ), (10) where τ is the temperature factor for controlling the softness of distribution, and we set τ = 0.5.

F.2 More visualizations

We visualize the student features, denoised student features, and teacher features in Fig. 7. First, by comparing the original student and teacher features, we can conclude that the discrepancy between student and teacher features is fairly large, and the student feature contains more noises and is not as salient as the teacher feature. While for the denoised feature generated by our Diff KD, it is very similar to the teacher feature, this infers that distillation on the denoised student feature and teacher feature can get rid of the noises that disturb the optimization.

Image Student Denoised student Teacher

Figure 7: Visualizations of student features, denoised student features and teacher features on COCO dataset.