BinaryDM: Accurate Weight Binarization for Efficient Diffusion Models
Authors: Xingyu Zheng
Xianglong Liu
Haotong Qin
Xudong Ma
Mingyuan Zhang
Haojie Hao
Jiakai Wang
Zixiang Zhao
Jinyang Guo
Michele Magno
Venue: ICLR 2025 Poster (2025)
Keywords: Model Quantization
Model Compression
Generative Model
Diffusion Model
Primary area: generative models
TL;DR: In this paper, we propose BinaryDM, which pushes the quantization of the diffusion model to the limit with binarized weight.

Abstract: With the advancement of diffusion models (DMs) and the substantially increased computational requirements, quantization emerges as a practical solution to obtain compact and efficient low-bit DMs. However, the highly discrete representation leads to severe accuracy degradation, hindering the quantization of diffusion models to ultra-low bit-widths. This paper proposes a novel weight binarization approach for DMs, namely BinaryDM, pushing binarized DMs to be accurate and efficient by improving the representation and optimization. From the representation perspective, we present an Evolvable-Basis Binarizer (EBB) to enable a smooth evolution of DMs from full-precision to accurately binarized. EBB enhances information representation in the initial stage through the flexible combination of multiple binary bases and applies regularization to evolve into efficient single-basis binarization. The evolution only occurs in the head and tail of the DM architecture to retain the stability of training. From the optimization perspective, a Low-rank Representation Mimicking (LRM) is applied to assist the optimization of binarized DMs. The LRM mimics the representations of full-precision DMs in low-rank space, alleviating the direction ambiguity of the optimization process caused by fine-grained alignment. Comprehensive experiments demonstrate that BinaryDM achieves significant accuracy and efficiency gains compared to SOTA quantization methods of DMs under ultra-low bit-widths. With 1-bit weight and 4-bit activation (W1A4), BinaryDM achieves as low as 7.74 FID and saves the performance from collapse (baseline FID 10.87). As the first binarization method for diffusion models, W1A4 BinaryDM achieves impressive 15.2x OPs and 29.2x model size savings, showcasing its substantial potential for edge deployment.

Published as a conference paper at ICLR 2025
BINARYDM: ACCURATE WEIGHT BINARIZATION FOR EFFICIENT DIFFUSION MODELS
Xingyu Zheng', Xianglong Liu Haotong Qin', Xudong Ma' Mingyuan Zhang?,
Haojie Jiakai Wang', Zixiang Zhao Jinyang Guo', Michele Magno² Beihhang University 2ETH Zürich
3Nanyang Technological University "Zhongguancun Laboratory XX''an Jiaotong University
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wangjkēzgelab. edu. on zixiang. zhannggghaaeeth.cc
ABSTRACT
With the advancement of diffusion models (DMs) and the substantially increased computational requirements, quantization emerges as practical solution to obtain compact and efficient low-bit DMs. However, the highly discrete representation leads to severe accuracy degradation, hindering the quantization of diffusion models to ultra-Iow bit-widths. This paper proposes a novel weight binarization approach for DMs, namely BinaryDM, pushing binarized DMs to be accurate and efficient by improving the representation and optimization. From the representation perspec- tive, present Evolvable-Basi Binarizer (EBB) enable smooth evolution of DMs from full-precision to accurately binarized. EBB enhances information representation in the initial stage through the flexible combination of multiple binary bases and applies regularization to evolve into efficient single-basis bina- rization. The evolution only occurs in the head and tail of the DM architecture to retain the stability of training. From the optimization perspective, a Low-rank Representation Mimicking (LRM) is applied assist the optimization of binarized DMs. The LRM mimics the representations of full pre-iireo DMs in low-rank space, alleviating the direction ambiguity of the optimization process caused by fine-grained alignment. Comprehensive experiments demonstrate that BinaryDM achieves significant accuracy and efficiency gains compared SOTA quantization methods of DMs under ultra-low bit-widths. With 1-bit weight and 4-bit activation (WIA4), BinaryDM achieves as low as 7.74 FID and saves the performance from collapse (baseline FID 10.87). As the first binarization method for diffusion models, W1A4 BM achieves impressive 15,2x OPs and 29.2 x model size savings, showcasing its substantial potential for edge deployment.
INTRODUCTION
Diffusion models (DMs) (Ho et al. 2020 Song & Ermon, 2019) have shown excellent capabilities in generation tasks in various fields, such as image (Ho
2020 Song & Ermon 2019 Song et al.)
2020b), vision (Mei & Patel 2023 Ho et al. 2022). and speech Miittal et al.) 2021 Popov et al. 2021 Jeong al. 2021). DMs have become one of the most popular generative model paradigms with sigmificant quality and diversity advantages. DMs generate data through the iterative noise estimates, while up to 1000 iterative steps slow the inference process and rely on expensive hardware resources. Although some proposed methods can effectively reduce the number of iterations to dozens of times (Song et al. 2020al Ran-Roman et al., [222]] Nichol & Dhariwal] 202T Bao al. (022). the complex neural network of DMs also results in large number of floating point calculations and memory usage in each step, which hinders the efficient deployment and inference on edge. Therefore, the compression of DMs has been widely studied practical technology to accelerate the iterative process and reduce the inference cost, including quantization (Li et al. 2023b] /hang et al. 2023).
distillation (Salimans & Ho 2022 Luo 2023 Meng et al. 2023), pruming (Fang et al. 2023 ) etc.
Low-bit quantization emerges as a practical approach to compress deep learning models by reducing
the bit-width of parameters (Yang al. 2019 Gholami et al. 2022 Qin al. 2024), and also has

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Evolvable-Ban Baawabbe-BBsssssee Binarizer
BinaryDM Framework
Low-ronk Representation Mimicking
My Regulariztionn
Evolvable
Vanilla
1-bot
Trein Shoge
Timestap Emieed Medule
Timestoo Embed Module
Tucsestep Enileed
Timestep Embed Module
camable
Detarminisãic
Figure I: Overview of BinaryDM consisting of Evolvable- Basis Binarizer enhance information representation and Low-rank Representation Mimicking to improve optimization direction.
satisfactory generality to various network architectures. Thus, with quantization, DMs can enjoy the compression and acceleration brought by fixed-point parameters and computation in inference (Li et al. 2023b a Shang et al., 2023). The 1-bit quantization, namely binarization. allows the binarized model to enjoy compact 1-bit parameters and efficient computation (Liu et al., 2020; Xu al.
2021b a). With the most aggressive bit-width, 1-bit weights can lead to up to 32x size reduction and
replace expensive floating- point multiplications with addition constructions during inference, thus
saving resources significantly (Rastegari et al. 2016 Frantar al., 2023).
However, binarized DMs suffer significant performance degradation compared to their full-precision counterparts. The performance decline primarily arises from two aspects: First, weight binarization severely restricts the feature extraction capability of diffusion models, causing significant damage to information in critical representations of generative models. Though several weight binarization methods strive to mitigate binarization errors and enrich representations by floating-por -oinnt scaling factors (Rastegari et al. 2016 Liu et al. 2020 Qin et al. 2023b /Zhang al. 2024). the number of candidate values for each weight still drops from 2 to 2 The limited informationnreeprseett capacity of binarized filters leads to severe loss when compressing from full-precision initialization to 1-bit binarization. This fact causes catastrophic consequences for DMs that highly require representation capacity. Second, introducing discrete binarization functions DMs poses significant hurdle to stable convergence. Existing ouantization-awal training methods for DMs usually employ direct output-based supervision ([.i et al.) 2023b He et al., (023). Binarization introduces significant errors in forward parameters and backward gradients, leading to disruptions in the optimization direction (Courbariaux et al., 2016). Learning the fine-grained details embedded in the synthetic features can contribute to the overall optimization process of binarized DMs. Unfortunately, the disruptive influence of extreme discretization becomes pronounced this context, rendering the convergence vulnerable to disturbances and, in some cases, seemingly unattainable.
In this paper, we propose BinaryDM DM to push the weights of diffusion models toward binarization. The proposed method pushes the weights of diffusion models toward accurate and efficient binarization, considering the representation and computation properties. BinaryDM applies quantization-awanl training to binarized DMs accurately for efficient inference, which takes the representation and computation properties of diffuusion models into account and is composed of two novel techniques: From the representation perspective, we present Evolvable-Basis Binarizer (EBB) to recover the representations generated by the binarized DM. EBB first applies dual sets of binary bases with learnable scalars significantly enhance the feature extraction capability of the initial binarized weights, then evolves the high-order bases to the single-basis form guided by regularization loss. It selectively applied only to key parameter locations of the DM architecture to reduce unnecessary evolution processes, casing the training burden and making the evolution smoother. From the optimization perspective, a Low-rank Representation Mimicking (LRM) incorporated to enhance the binarization-awar optimization of diffusion models. LRM projects binarized and full-precision representations to low-rank, enabling the optimization of binarized DM to focus on the principal direction and mitigate direction ambiguity caused by the representation complexity of generation.
Comprehensive experiments show that our proposed BinaryDM has significant accuracy and efficiency gains compared to DMs binarized by existing SOTA binarization and low-bit quantization methods.
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Our BinaryDM can consistently outperform the baseline DDIM and LDM with binary weight, especially with ultra-low bit-width activation. For example, on CIFAR- 10 32 x DDIM, the precision metric of BinaryDM even exceeds the baseline by 9.46% (baseline 5.92 vs. BinaryDM 6.48) with 1-bit weight and 4-bit activation (W1) A4), saving the binarized DM from collapse. BinaryDM even outperforms the higher bit-width SOTA quantization methods of DM. For LDM-8 on -Sh-Churee 256x256, W1A4 BinaryDM exceeds W4A4 EfficientDM in the FID metric by 4.43. As the first binarization method for DMs, BinaryDM yields impressive 15.2x and 29.2x savings on OPs and model size, demonstrating the vast advantages and potential for deploying the DM on edge.
2 RELATED WORK
Diffusion models (DMs) demonstrate outstanding performance across diverse range of tasks (Ho
et al. 2020; Song Ermon 2019 Song et al. al. 2020b; Niu et al. 2020) Mittal et al., 2021 Popov et al.
2021 Jeong al. [021; Peebles & Xie 2023). However, their slow generation process presents
significant challenge to widespread implementation. Substantial research has focused on reducing the
number of time steps to expedite the generation process (Watson et al. 2021 Chen et al. 2020 Song
& Ermon 2019 Song et al. 2020b Feng et al. 2024b). Despite the reduction in time steps, the noise estimation network of DMs still demand expensive computation and memory for each step.
Quantization and binarization are explored widely as popular compression techniques (Nagel et al.
2020: Lin et al. 2021). These methods involve quantizing the full-precision parameters lower bit- width (e.g., 1-8 bit). By converting floating-point weights and activations into quantized values, the model size can be significantly reduced. This size reduction decreases computational complexity and substantially improves inference speed, memory usage, and energy consumption savings (Shang et al. training (Gholami et al.) 2022 Qin et al. 2020 Yang et al. (019)) involves compressing DMs within a training/fine-tniing pipeline to update parameters (Li et al., [023b] He et al., (023). Despite these advancements, achieving 1-bit quantization for the weights of DMs remains formidable challenge. This underscores the need for further research to unlock the potential benefits of 1-bit binarization DMs. Appendix presents more details about related works.
2023 Li al. 2023a). One notable technique, quantization-awa
BINARYDM
3.1
PRELIMINARIES
In the forward process of diffusion models, Gaussian noise is added to data q(x) in T times via a schedule 3r controlling noise strength, the process can be expressed as
q (a. xt-1) = N (z: v 1,11
(1)
where x, E {x1..... ØT} denote the noisy samples at t-th step. The reverse process aims to generate samples by removing noise, approximating the unavailable conditional distribution (x,-1 x)) with learned distributions Po (x,-1 xx), which can be expressed as
pa (x 1 xx)) = N ii (I,, t) 3,1)
(2)
The mean go (xr, 1) and variance 3, could be derived using the reparameterization (Ho et al. 2020
a+ es (z2,
3. ā,- Se.
poo (xi, t) Vog x V1 az
ā.
where 02 ā, = I 0g,, and eg denotes function approximation with the learnable parameter 0, which predicts from Ht. The U-Net with spatial transformer layers is applied as the architecture of the noise estimation network in common practices. For the training DMs, a simplified variant of the variational lower bound is usually applied as the loss function achieve high sample quality, which can be expressed as
Lample = Er. [|E, 6n (Vanito + /1 aret, 1)1
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lteration=O
Iteration=200 200
Iieration=400
Iteration 600
Buodey
Raucke
K2-220
Frequency
15
15
15
25
-2.00 9/6
-.10
0.10
Binarized Weight
Figure 2: Comparison of binarized weights(channel- broader representation range at the early stage and then gradually transitions to single-basis state, while the quantitative information entropy H. further illustrates its enhanced representation capacity.
for convolutional layer. EBB possesses
The binarization and quantization compress and accelerate the noise estimation model by discretizing weights and activations to low bit-width. In the baseline of the binarized diffusion model, the weight E 0 binarized to 1-bit by w o sign(w) (Rastegari et al. 2016; Courbariaux et al. 2016), where sign function confine w to +1 or 1 with O thresholds, w E U denotes the binarized weight, and 9 denotes the binarized noise estimation network. a the floating-poing scalar, which is initialized as |||||| (n denotes the number of weight elements) and learnable during training process following (Rastegari et al. 2016 Liu al. 2020). The activation is quantized by the LSQ quantizer (Esser et 2009). With the 32x compressed weight, the computation of noise estimation can also be replaced with integer additions, achieving significant compression and acceleration.
3.2 B.A.VALLE-BAIIS BINARIZER
In the current baseline, weights are quantized to I-bit values to economize on storage and computation during inference, and activations can be quantized to integers. However, the extensive discretization of weights to binary in DMs results in a notable deterioration of the generated representations. The bit-width of each weight element is limited the original 32. significantly restricting the information- carrying capacity of DMs. Previous works present a straightforward approach that enhances binarized parameters via higher-order residual bases (Li et al. 2017; Huang et al.) 2024a; Chen et al.) 2024a) have achieved significant success in terms of accuracy, but the introduced additional bases result in substantial additional hardware overhead, making them unsuitable for practical deployment on existing hardware architectures. While these methods do not achieve full binarization, they significantly help the model approach full-precision performance.
These findings led to consider the significance of higher-order residual binarization for DMs, as it notably enhances the information space and improves representational capacity. To utilize the representation capability of high-order bases while avoiding redundant costs during inference, we sought to use residual binarized structures as transitional structures and evolve during training. This would allow fully binarized DMs to start from more favorable initial state, resulting in a smoother optimization process and better final outcomes.
We propose the Evolvable-Base Basis Binarizer (EBB) address the adaptation challenges binarized DMs face during the early optimization stages due to structural limitations. EBB is implemented in two stages during training. The first stage uses higher-order residual multi-basis with regularization penalties, then transitions into the second stage with simple single-basis binary weights.
Learnable Multi-Basis. In the forward propagation of the first stage, EBB is defined as
whe = dj sign (w) + σn sign (w - σ1 sign (w)),
(5)
where the or and oy are learnable scalars which are initialized as of ||||| and o 1 sign(w]]] respectively, || denotes the f2-normalization. The inference of layer binarized by EBB involves the computation of multiple bases. For instance, the convolution in binarized DM is
= a x WEBB = o) (a @ sign (w)) + on (a @ sign (w σ1 sign (w))).
(6)
where a denotes the activation, and x and @ denote the convolution consisting of multiplication and addition instructions (Rastegari et al. 2016 Hubara et al. 2016). respectively.
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In the backward propagation of EBB, the gradient of the learnable scalars is calculated as follows:
BweEBB
sign (w) (1 on sign (w)). if oj sign (w) E (w + 1),
(7)
do1
sign (w)
otherwise,
EBB
sign (w 01 sign (w)), don
(8)
where the Straight Through Estimator (STE) is applied approximate the sign function during backward. With the binary basis with different learnable scalars, the representation capability of quantized weights can be significantly enhanced. The residual initialization makes the optimization of binarized DM start from an error- mirro-mmiiiizing state. As presented in Figure [ at the initialization iteration-O. EBB exhibits significantly higher information entropy and richer representational space. With EBB, the representation of weights is considerably more diversified than the binarized DM baseline, providing more favorable initialization state for optimization.
Transition Strategy. We adopt two-stage training process with regularization strategy, allowing the DM to transition from an initial multi-basis structure to full binarization. In the first stage, regularization loss is applied to the higher-order learnable scaling factors, encouraging them to approach zero:
1
LEBB =
Σ i
where N denotes the number of basic layers (e.g., convolutional, linear) in the noise estimation network of DMs, and r are hyperparameter coefficients used to balance the loss terms, typically set to 9e-2.
In the second stage, all higher-order terms are removed, and the forward propagation is simplified to:
wh = σj sign (w).
(10)
Through regularization penalties, EBB can smoothly evolve from an initially more information-rie -ich residual state to a single-basis state suitable for inference. As shown by the evolution process in 2 the dequantized weights of EBB gradually converge with full binarization as iterations progress. However, EBB consistently retains more information throughout the process, making the overall optimization of the binary DM easier.
bimodal distribution consistent
Location Selection. In our Din the proposed EBB is partially applied to crucial and parameter- sparse locations of the diffusion models while retaining concise vanilla binarization at other locations to reduce unnecessary evolution processes and the associated training overhead. Specifically, we apply EBB where the feature scale is greater or equal to _ input scale, í.e., the first and last six layers with only the 15% of whole parameters in the noise estimation network of BinaryDM. In contrast, other layers keep consistent with the binarized DM baseline with vanilla binarizers. On the one hand, applying EBB to these key parameter locations within DM architectures significantly enhances the information processing capacity of binarized DMs in the early stages of optimization, leading to better overall learning process. On the other hand, using a vanilla binarizer for intermediate layers, which contain the most parameters but are less sensitive to quantization loss, reduces the instability caused by switching between stages for unimportant components and lowers the training overhead.
3.3 LOW-RANK REPRESENTATION MIMICKING
In the quantization -ware training of DMs, the discretization of parameter space caused by weight binarization and activation quantization function and the inaccurate gradient approximation involved in the derivation process bring difficulties to the stable convergence of binarized DM. Since having almost the same architecture, the original full-precision DM can be regarded as an oracle of the binarized one. Therefore, intuitive approach is to assist the training of binarized DMs by mimicking the representation of full-precision replicas. During training, aligning outputs and intermediate representations of binarized DMs with full-precision counterparts can provide additional supervision, accelerating the convergence of quantized DMs significantly.
However, there issues directly aligning the intermediate representations of binarized and full- precision DMs during optimization. Firstly, fine- -ra-nga aligument of nigh-dimensional representa- tion leads to a blurry optimization direction for DMs, especially when mimicking the intermediate
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6 No Distillation
TimosxeBBlock12
1locste
Tincksop
3.00
5.00
12.70
0.90
MSE
Fy-Distmnee
LRM
4.60
2.20
4.20
10:30
0.70
1.92
3.80
8:80
0.60
1.56
VW
3.40
7.50
0.50
1.20
3.00
6.20
0.40
2c4
Training Iteration
Figure 3: The impact of different distillation loss functions on the output features of each block in both full-precision DM and binary DM, measured by the C2 distance. Our proposed LRM enables the binarized DM to have the best information- mintiiionmiiiiiinggg capability.
features is introduced. Secondly, compared to the full precision DM, the intermediate features in the binarized one are derived from a discrete latent space since the discretization of parameters makes difficult mimic the full-precision DM directly.
Therefore, we propose Low-rank Representation Mimicking (LRM) to efficiently optimize the BinaryDM by mimicking full- full-precision representations in low-rank space. We group the full- precision DM DF based on the timestep embedding modules composed of residual convolution and transformer blocks. The intermediate representation can be denoted e (æx,() E R We use principal component analysis (PCA) to project representations to low-rank space. The covariance matrix for representations of the full-precision DM is
1
sPP (h x w)² So, (xt, 1) EB.
FPT t)),)),
(11)
where 0g represents the composition of the top i modules. The eigenvector matrix E, E Rexe is
E, E,T,E, A;:
(12)
where A; is the diagonal matrix of eigenvalues of C,, arranged in descending order. We take the matrix composed of the first x column eigenvectors of Eg as the transformation matrix, denoted E, & where [-] denotes the round function and K denotes the reduction times of dimension. We use E. to project the intermediate representation of both full-precision and binarized:
FP (zz, t) = FP
(It, t) E! f hi (x . t) = E (Iz, t) E.
(13)
where eb, (æe, denotes the intermediate representation of the i-th layer in the DM with binarized parameters gh. and R FP (æt, t) and R (æ,, t) denote the low-rank representations of full-precision and binarized DMs, respectively, with the same shape h w J. The K empirically defaults as 4 and is detailed ablated in Appendix B.2
We then leverage the obtained low-rank representation to drive the binarized DM to learn the full- precision counterpart. We construct a mean squared error (MSE) loss between the i-th module of low-rank representations between full full-precision and binarized DMs:
LLRME
R
R
(14)
The total loss function is composed of Eq Eq and Eq
14
Livaal Esimple + LEBB X M Σ LLRME
(15)
where M denotes the number of timestep embedding modules in the noise estimation network of DMs, and À is hyperparameter coefficient to balance the loss terms, typically set to lc-4.
Since the computation cost of obtaining the transformation matrix E fc. in LRM is significantly expensive, compute the matrix by the first batch of input and keep it fixed during the training

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Bascline
BinaryDM
Figure 4: Visualization of samples generated by the binarized DM baseline and W1A4 BinaryDM.
Table I: Comparison for unconditional generation CIFAR-10 10 32 32 by DDIM with 100 steps
Method
#Bits
ISt
FID
sFID
Prec.t
FP
32/32
8.90
5.54
4.64
67.92
LSQ
2/32
8.17
18.56
8.30
59.22
Baseline
1/32
7.84
22.59
6.83
60.23
BinaryDM
1/32
8.28
11.92
5.42
61.84
LSQ
2/8
7.64
29.66
30.63
58.76
Baseline
7.94
20.25
59.42
BinaryDM
1/8
8.47
11.21
5.49
62.65
LSQ
2/4
4.04
137.75
43.68
40.74
Baseline
1/4
5.92
100.17
51.06
36.46
BinaryDM
1/4
6.48
87.77
51.73
37.25
process. The fixed mapping between representations is also beneficial to the optimization of binarized DMs from stability perspective, updates to the transformation matrix could significantly alter the direction of binary optimization, which would be disastrous for DMs with high demands for representational capacity and optimization stability.
LRM enables binarized DMs to mimic the representation of full-precision counterparts, improving the optimization process by introducing additional supervision. As shown in Fig 3 LRM effectivell brings the local block closer to the full- preccioonn block. Furthermore, by applying low-rank projec- tions based on the principal components from full-precision representations before representation mimicking, the binarized DM can be optimized along clear and stable directions, accelerating the convergence of the model. Furthermore, binarized and full- full-precision DMs have entirely consistent architectures, making representation mimicking between them natural.
EXPERIMENT
We conduct experiments on various datasets, including CIFAR- 32 32 (Krizhevsky et al. 2009). LSUN-Bedroome Bedrooms 256 x 256 Yu et al., 2015). 256 256 (Karras al. 2019) and ImageNet 256 256 (Deng et al. 2009). for both unconditional and conditional image generation tasks over DDIM and L.M.. The evaluation metrics used in our study encompass Inception Score (IS), Fréchet Inception Distance (FID) (Heusel et al., 2017). Sliding Fréchet Inception Distance (sFID) (Salimans et al. 2016), and Precision-and -eie-annd-Rea-l-ll We implement and evaluate the DMs binarized by our BinaryDM and the baseline presented in Section 3.1 where
256 x 256 Yu et al. 2015). FFHQ
LSQ (Esser et al. 2019) is employed uniformly activations quantizers. Several SOTA quantization methods for DMs with 2-8 bits weights are also considered (He et al. 2023 et al. 2023a So
al. 2024). Detailed settings are presented in Appendix B.I
4.1
MAIN RESULTS
Unconditional Generation. We first conduct experiments the CIFAR-10 dataset. As shown in
[ the binarized DM bascline suffers a severe breakdown this low-resolution scenario, while method significantly recovers the performance. Under the A4 bit-width, BinaryDM surpasses
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Table 2: Results for LDM on multiple datasets unconditional generation by DDIM with 100 steps.
Model
Dataset
Method
#Bits
Sizermu>
FID
sFID
Precisiont
Recallf
FP
32/32
1045.4
3.09
7.08
65.82
45.36
LSQ
2/32
69.8
7.49
12.79
64.02
37.60
Baseline
1732
33.88
8.43
13.11
663.45
29.88
BinaryDM
1/32
35.8
6.99
12.15
67.51
36,80
Q-Diffusion
278
69.8
62.01
33,56
16.48
14.12
LSQ
2/8
69.8
6,48
11.66
62.55
38.92
LSUN-Bedroome
LSUN- Bedrooms
Baseline
1/8
35.8
9.37
12.10
64.36
30.76
LDM-4
256 256
BinaryDM
1/8
35.8
6.51
11.67
65.80
35.28
O-Diffusion
4/4
134.9
427.46
277.22
0.00
0.00
EfficientDM
4/4
134.9
10.60
LSQ
2/4
69.8
12.95
12.79
55.97
34.30
Baseline
1/4
35.8
10.87
15.46
64.05
26.50
TDQ
1/4
35.8
11.28
12.80
55.14
27.32
ReAetNet
1/4
35.8
10.23
13.02
61.43
29.68
Q-DM
1/4
35.8
9.99
11.96
57.62
29.30
INSTA-BNN
1/4
35.8
9.42
12.39
60.05
31.08
BI-DifiSR
1/4
35.8
8.58
11.81
62.61
30.86
BinaryDM
1/4
35.8
7.74
10.80
64.71
32.98
FP
32/32
1125.2
4.82
17.66
75.18
46.80
LSQ
2/32
74.1
8.16
19.87
74.98
35.76
Baseline
1/32
38.1
9.91
17.94
74.89
26.88
BinaryDM
1/32
38.1
8.14
17.44
75.51
34.56
Q-Diffusion
74.1
201.23
238.70
2.39
8.60
LSQ
2/8
74.1
8.11
19.25
77.04
34.98
LSUN-CHI JUUNChurches
LDM-8
Baseline
1/8
"8..I"
10.94
16.95
77.300
25.66
256 256
BinaryDM
1/8
38.1
8.63
15.13
77.74
33.48
EflicientDM
144.2
14.34
Q-Diffusion
144.2
198.35
184.43
5.48
0.12
LSQ
2/4
74.1
10.00
19.08
74.93
25.80
Baseline
1/4
38.1
12.98
21.55
70.78
25.30
BinaryDM
1/4
38.1
9.91
18.04
73.72
29.96
FP
32/32
1045.4
6.64
14.16
76.88
S0.82
Q-Diffusion
4/32
134.9
11.60
10.30
Baseline
1/32
35.8
10.49
11.56
72.64
39.62
BinaryDM
1/32
35.8
8.70
9.68
73.92
42.22
FFHQ
Q-Diffusion
878
265.0
10.87
10.01
LDM-4
256 256
Q-Diffusion
4/8
134.9
11.45
9.06
Baseline
1/8
33..8
10.79
10.77
73.20
41.00
BinaryDM
1/8
35.8
9.58
10.74
74.48
41.75
Baseline
1/4
35.8
15.07
12.48
74.34
35.12
BinaryDM
1/4
35.8
12.34
11.18
74.83
38.09
the binarized baseline by 9,46% in IS metrics on the CIFAR-10 and outperforms the LSQ under W2A4, where the latter involves several times of computation and storage.
Our LDM experiments encompass the evaluation of LDM-4 on LSUN-Bedrooms and FFHQ datasets, along with the assessment of LDM-8 the LSUN-Churches dataset. The experiments utilized the DDIM sampler with 100 steps, and the detailed outcomes are presented in Table 2 We showcase results across various activation bit widths in the context weight binarization. comparing them with the outcomes of some quantization methods at higher bit settings. The conventional binary baseline method exhibits subpar performance in the LDM context and experiences a further decline dataset. In contrast,
in the W A1 experimental setup, particularly noticeable in the BinaryDM significantly enhances the generation quality, especially for LDM-4, exhibiting consistent performance across different activation bit settings. Notably, when compressing from W1A32 to W1A4 on the BeUNN-Be dataset, the FID increased by a mere 0.75 for BinaryDM, showcasing its robustness. From the evaluation results of LDM-4 on FFHQ datasets, it can be observed that BinaryDM DM outperforms all other methods under various settings in terms sFID, even surpassing W8A8 O-Diffusion with bit-wite width of W1A8. Moreover, BinaryDM demonstrates more significant
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Table Results on ImageNet 256
256 in conditional generation by DDIM with 20 steps.
Sampler
Method
#Bits
IST
FID
sFID
Prec.1
FP
32/32
235.84
12.96
25.99
92.63
Baseline
1732
197.85
11.50
23.44
84.83
BinaryDM
1/32
215.55
10.86
21.10
88.43
DDIM
Baseline
I/8
203.90
I1.35
25.49
85.78
BinaryDM
1/8
211.43
11.23
24.12
88.09
Bascline
1/4
187.70
T1.51
20.77
84.13
BinaryDM
1/4
208.42
10.78
20.40
87.61
FP
32/32
247.38
13.54
18.85
94.22
Baseline
1732
2I1.69
I1.23
21.32
86.16
BinaryDM
1/32
226.86
11.00
19.01
91.17
PLMS
Baseline
1/8
205.58
12.78
21.57
84.07
BinaryDM
1/8
225.18
11.33
19.18
90.35
Bascline
1/4
193.1I
11.08
23.21
81.40
BinaryDM
1/4
218.06
10.36
18.85
88.74
FP
32/32
242.27
13.10
19.82
93.53
Baseline
1/32
203.98
11.22
23.49
83.52
BinaryDM
1/32
214.91
11.07
20.61
87.71
DPM-Solver
Bascline
T/8
T88.21
T2.83
25.07
80.14
BinaryDM
1/8
216.27
11.68
20.52
88.36
Baseline
1/4
178.47
11.67
26.72
77.27
BM
1/4
206.80
10.83
20.68
85.34
advantages at lower activation bit-widths, achieving accurate generation with an FID of 12.34 under 4-bit activation. BinaryDM even approaches the generation quality of the full-precision model, with specifically generated image examples provided in Appendix B.3
Conditional Generation. For conditional generation, the performance of our BinaryDM evaluated on the ImageNet dataset with resolution of 256 x 256, focusing on LDM-4. We employ three distinct samplers to generate images: DDIM, PLMS, and DPM-Solver. The results Table underscore the DDIM, surpassing the baseline consistently across
remarkable effectiveness of our BinaryDM, almost evaluation metrics and even outperforming the full-pre full-precision diffusion model in several cases. The binarized DM baseline performs relatively stable in configurations W1A32 and W WA8 but significantly declines under W W1A4, with the IS decreasing to 187.70 when using the DDIM sampler. In contrast, BinaryDM maintains
IS of 208 42 in W1A4. Specifically, when utilizing the DPM-Solver sampler, the IS plummets to 178.47, and the sFID experiences sharp increase to 26.72 In stark contrast, our binarized DM maintains consistently high performance, achieving 206.80 IS and 20.68 FID and outperforming the baseline in most scenarios.
4.2 ABLATION STUDY
We perform comprehensive ablation studies for LDM-4 the LSUN-Bedrooms dataset evaluate the effectiveness of our proposed EBB and LRM, and the results are presented in Table 4
The performance has shown significant recovery when first applying our EBB to binarized diffusion models, with the FID decreasing from 8.43 to 7.39. This confirms that the degradation in parameter representational capacity due to binarization is primary performance bottleneck in the binarized DM baseline. Solving this representation degradation is prerequisite for improving model performance. From a structural perspective, EBB provides binarized diffusion models with an initial state with higher information capacity, alleviating the degradation of representational ability in the early stages and guiding QAT toward a more easily optimizable direction.
With the application of LRM this basis, the generative capability of the resulting binarized diffusion models is further enhanced, with the FID decreasing to 6.99. This indicates that the low-rank mimicking scheme, designed from feature-matching perspective, effectively utilizes the representational information of the full-precision model, achieving supervision and alignment of intermediate features and better guiding the optimization of the binarized diffusion models.
Further substantiating this view, the detailed ablation experiments in Appendix B.2 delve into an in-depth discussion of the specifies concerning EBB and LRM. Combining these two techniques in

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Table 4: Ablation results on LSUN-Beddoomn 256 x 256.
Method
#Bits
FID
sFID
Prec.
Recall
FP
32/32
3.09
7.08
65.82
45.36
Vanilla
1/32
8.43
13.11
63.45
29.88
+EBB
1/32
7.39
12.34
65.98
35. 85.84
+LRM
1/32
6.99
12.15
67.51
36.80
BinaryDM can significantly enhance performance, emphasizing that better optimization process can improve the quality of generation when ensuring accurate representation.
4.3 EFFICIENCY ANALYSIS
For inference, we demonstrate the size and OPs of BinaryDM under different activation bit- The results in Table indicate that our DM can achieve up to 29. 2x space savings while obtaining up to 15.2x acceleration during inference, fully harnessing the advantages of binary computation. BinaryDM achieves optimal inference efficiency while surpassing the performance of advanced methods with higher bit widths. The W WIA BinaryDM achieves lower FID compared to the W4A4 EfficientDM, while its model size and OPs are only 26.5% and 25.9% of the latter, respectively.
For training, while the training process for binarized DM typically incurs higher overhead compared to post-training quantization methods, practical observations reveal that our approach offers productivity advantages across various models and datasets. As shown in Table 6 despite having a training time shorter than the calibration time required by Q-Diffusion, our method attains significantly superior generation quality, particularly at lower bits.
Table 5: Inference efficiency of our proposed Bi of LDM-4 LSUN-Bedrooms 256 x 256.
Model
Method
#Bits
Size
OPs
FIDL
Full-Precision
4/4
1045.4
96.0
3.09
O-Diffusion
4/4
134.9
24.3
427.46
LDM-4
EfficientDM
4/4
134.9
24.3
10.60
LSQ
2/4
69.8
12.3
12.95
BinaryDM
1/4
35.8
6.3
7.74
Table Training time-cost of BinaryDM compared to the advanced PTQ method.
Dataset
Method
#Bits
Size
Timeas
FID
O-Diffusion
4/4
134.9
13.7
427.46
BinaryDM
1/4
35.8
11.3
13.93
Q-Diffusion
4/4
144.2
10.9
198.35
L.SUN-Churches
BinaryDM
1/4
38.1
9.0
15.11
5 CONCLUSION
In this paper, we propose BM, a novel accurate quantization-awar training approach to push the weights of diffusion models towards the limit of binary. Firstly, present an Evolvable-Basic Binarizer (EBB) to enable the QAT of binarized DMs to start from a more favorable initial state, leading smoother optimization process and better final results. Secondly, Low-rank Repre- sentation Mimicking (LRM) is applied to enhance the binarization-awan optimization of the DM, alleviating the optimization direction ambiguity caused by fine- fine-grained alignment. Comprehensive experiments demonstrate that Bi achieves significant accuracy and efficiency gains compared the first binarization method for diffusion models, W1A4 BinaryDM achieves impressive 15.2x OPs and 29. x9.2x storage savings, showcasing substantial advantages and potential for deploying DMs on edge.
to SOTA quantization methods DMs under ultra-low bit-widths.
Acknowledgement This work was supported by the Beijing Municipal Science and Technology Project (No. 1201000003)2300), the National Natural Science Foundation China (Nos. 62306025, 92367204), CCF-Baidu Open Fund, Beijing Natural Science Foundation (QY24138). the Swiss National Science Foundation (SNSF) project 200021E 219943 Neuromorphic Attention Models for Event Data (NAMED), and Baidu Scholarship.
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A DETAILS OF BINARYDM
Diffusion Models have showcased remarkable performance across a diverse array of tasks (Ho
al. 2020: Song & Ermon 2019; Song et al. 2020b; Niu al. 2020; Mittal et al. 2021 Popoy et al., 2021 Jeong et al. (021). These tasks involve a forward Markov chain process, wherein generated noisy samples are incrementally added through Gaussian noise. Subsequently, reverse denoising process refines these samples, producing high-fidelity images. However, the diffusion model's slow generation process poses a significant challenge to widespread implementation. To address this issue, substantial research has concentrated on reducing the time steps required for diffusion model generation. Techniques such as trajectory search can be formulated as dynamic programming problems (Watson et al. 20221,, and grid search has demonstrated the ability to discover effective trajectories within a mere six- six-time steps (Chen et al.) 2020). Moreover, the introduction of non-Markov diffusion processes has been instrumental in expediting sampling during the reverse process (Song & Ermon 2019; Song et al. 2020b). with the application of numerical methods to solve associated equations resulting in a notable reduction in the number of iterations to just a few dozen. Efforts to address these challenges have led to exploring faster step size schedules for VP diffusions, demonstrating the ability maintain relatively good quality and diversity metrics (San Roman et al. (021). Additionally, analytical approximations have been derived to simplify the generation process (Bao et al., 2022). These developments mark strides towards enhancing the efficiency and practicality of diffusion models in various applications. Despite these advancements, the denoising models still involve a considerable number of parameters, demanding substantial computation and memory resources for each denoising step. This computational expense hinders the practical implementation of the inference process on standard hardware.
Quantization and Binarization are popular compression approaches (Nagel et al. 2020 ?: ?: Lin
et al. 2021 Huang et al. 2024b Qin et al., 2023a). which quantize the full preciiiieinnn parameters of the neural network to lower bit-width (e.g.. 1-8 bit). By converting Moating-poini weight and activation into quantized ones, the model size of the neural network can be decreased, and the computational complexity can also be reduced, leading significant inference speedup, memory usage savings, and lower energy consumption. Model quantization methods for diffusion models are generally divided into two categories based on their pipeline and resource access during training or fine-tuning; fost-training quantization (Shang et al.
[2023] Li et al. 2023a) and quantization-awan training (Li et al. [223b] He al. 2023) Feng et al.] 2202aa. P. As a training- free method, post-training
quantization is considered more practical solution to obtain quantized models at low cost by searching for the best scaling factor candidates and optimizing the calibration strategy. However, the diffusion models quantized by post-training methods dramatically degrade generation quality (Shang ct al. 2023 Li et al. 2023a). Thus, quantization-awee aware training emerges for pushing quantized neural networks to higher accuracy (So et al. 2024|] Li ct al. 2023b He et al. 2023). Benefiting from the training/fine-tuning
process with sufficient data and training resources, the low-bit diffusion model obtained by quantization-awan training methods usually achieves higher accuracy than post-training ones. However, binarization for the weight of diffusion models is still far from available since it suffers serious accuracy degeneration challenges in existing methods.
B EXPERIMENTS AND VISUALIZATION
B. EXPERIMENT SETTINGS
Experimental Hardware. All our experiments were conducted on a server with Intel Xeon Gold 6336Y 2.40@ GHz CPU and NVIDIA A100 40GB GPU.
Models and Dataset. We perform comprehensive experiments encompassing unconditional image generation and conditional image generation tasks on two diffusion models: pixel-space diffusion model DDIM and latent-space diffusion model LDM. Specifically, we conduct experiments on DDIM using the CIFAR-I0 dataset with a resolution of 32 x 32. For LDM, our investigations spanned multiple datasets, including LSUN-Bedee Bedrooms, 256 x 256. Furthermore, we employ LDM for conditional image generation the ImageNet dataset with a resolution of 256 x 256. This diverse set of experiments, conducted on different models, datasets, and tasks, allows to comprehensively validate our proposed method's effectiveness.
JUUNChhrchess and FFHQ, all with a resolution of
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Proposed Quantization Baselines. We use per-channel quantizers for weights and per-layer quan- tizers, as is a common practice. To the best of our knowledge, the weights of the diffusion model have not yet been binarized, and found in our initial attempts that the basic BNN without scaling factors would collapse directly at the beginning of training. Hence, we utilize the fundamental binary quantizer, outlined in Section [3.1] as the baseline for weight quantization. LSQ serves as the foundational method for activations quantization. Under the uniform premise that the weights are binarized, we use variety of quantization bit-widths for activations cover as many realistic situations as possible. It's crucial to emphasize that we only quantize the diffusion model without quantizing the VAE part of the LDM. Additionally, we quantized the layers closest the input and output to 8-bit, adhering to common practice in this context.
Compared Advanced Strategies. In addition to the Baseline strategy we constructed, we also compared BinaryDM against advanced general binarization strategies and quantization strategies for diffusion models. The advanced general quantization strategies include the low-bit approach
LSQ (Esser et al. (2019), as well as binarization strategies such as ReActNet (Liu et al. 2020) and
INSTA-BNN (Lee et al. (023). Quantization strategies for diffusion models include the PTQ strategy O-Diffusion (Li et al. (023a) and QAT strategies such as EfficientDM (He et al.) 2023), Q-DM (Li al. 2024). TDQ (So et al. 2024), and BI-DiffSR (Chen et al.. 2024b). These comparisons with advanced methods highlight the effectiveness of BinaryDM.
Pipeline and hyperparameters. Our quantization-awar training (QAT) is based on the pre-trained diffusion model, and the quantizer parameters and latent weights are trained simultaneously. The overall training process is relatively consistent with the original training process of DDIM or LDM. Relative the training hyperparameters of the full precision model, we adjust the learning rate, reducing it to one-tenth to one-hundredth of the corresponding rate in the original full precision training script, especially on certain datasets, such as CIFAR- 10 and ImageNet. For DDIM training. we set the batch size to 64, while for LDM training, the batch size is configured as 4. Typically, models are trained for around 200K iterations.
Evaluation. To assess the generation quality of the diffusion model, we utilize several evaluation metrics, including Inception Score (IS), Fréchet Inception Distance (FID), Sliding Fréchet Inception Distance (sFID), and Precision-and-Recs Recall We randomly generate 50,000 samples from the model in each evaluation and compute the metries using reference batches. The reference batches used to evaluate FID and sFID contain all the corresponding datasets, while only 10,000 images were extracted when Precision and Recall were calculated. These metrics are all evaluated using ADM's TensorFlow evaluation suite.
Efficiency. We utilize Time and OPs as metrics for evaluating training efficiency and theoretical inference efficiency, respectively. For OPs, taking the convolutional unit an example, the BOPs definition for binary convolution operations is as follows (Yang et al. 2024 Wang et al.) (021):
BOPs Re whmnk baa bw.
(16)
It is composed of b,p bits for weights, bn bits for activation, input channels, output channels,
k x l convolutional kernel, and output dimensions of width w and height h for each channel. As there might also be full-precision modules in the model, the total OPs of the model are summed up according to the following method (Bethge et al. 2020):
OPs = 1
(17)
B.2 ADDITIONAL RESULTS
Further Ablation Study on W1A4. The ablation experiments in our main text were conducted on W1A32, as the highlight of BinaryDM lies achieving weight binarization for DM, with the activation quantization method always using naive scheme without any additional complex techniques. Here, we also supplement the ablation results on the more efficient W1A4 model. As shown in the Table 7 when EBB was added alone, the generative performance of the binary DM improved significantly, with the FID decreasing from 10.87 to 8.53. After adding LRM, the FID further decreased to 7.74, clearly illustrating the effectiveness of their synergistic effect.
Effects of EBB. We conducted comprehensive experiments on various aspects of EBB's specific details to validate its effectiveness further.
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Table 7: Ablation results on LSUN-Bedrooms 256 256.
Method
#Bits
FID
sFIDL
Prec.t
Recallf
FP
32/32
3.09
7.08
65.82
45.36
Vanilla
1/4
10.87
13,46
64.05
26.50
+EBB
1/4
8.53
11.99
62.94
30.78
+LRM
1/4
7.74
10.80
64.71
32.98
As supplement to the ablation study on the final generation performance (Table 4) in the main text, we present in Table the changes in training loss (Lsimple) at different iterations. The results indicate that EBB consistently achieves lower training loss, demonstrating its benefits for convergence.
Table 8: Training loss (Lsimple) different iterations LSUNN--edroone comparing the baseline and the addition of EBB.
Iterations
Method
#Bits
lel
le2
le3
le4
le5
Baseline 1/32
0.388
0,303
0.277
0.227
0.158
+EBB
1/32
0.352
0.264
0.242
0.206
0.151
The results in Table and Table 10 demonstrate that applying EBB significantly improves the generative quality of binarized diffusion models, highlighting the effectiveness of EBB. Furthermore, not applying EBB to the Central Parts yields better optimization results. The results Table TT demonstrate that applying EBB significantly improves the generative quality of binarized diffusion models, highlighting the effectiveness of EBB. Furthermore, not applying EBB to the Central Parts yields better optimization results. This suggests that applying EBB only to the key parts reduces the number of parameter updates when transitioning to the second stage, thus leading to a more stable optimization process for binarized diffusion models. Specifically, applying EBB to regions with high parameter counts but lower sensitivity to binarization can lead to suboptimal optimization stability, resulting worse performance compared applying EBB selectively. Additionally, while Head and Tail Parts (12) achieves lower training loss in the first 1000 iterations compared to Head and Tail Parts (6), its weaker transition full weight binarization results in higher loss 100K iterations. This suggests that applying EBB only to the key parts reduces the number of parameter updates when transitioning to the second stage, thus leading to more stable optimization process for binarized diffusion models.
Table 9: The impact EBB application scopes on L.SUN-Bedroodd (1/2), where Head and Tail Parts refers to how many of the first and last Timestep Embed Blocks and Central Parts refers to the middle Blocks.
Iterations
Head and Tail Parts
Central Parts
#Bits
le1
1e2
1e3
le4
1e5
0
1/32
0.335
0.291
0.268
0.202
0. 0.1
0
1/32
0.335
0.263
0.230
0.184
0.138
0
1/32
0.332
0.238
0.199
0.178
0.130
1/32
0.331
0.223
0.201
0.183
0.133
12
1
1/32
0.331
0.225
0.197
0.188
0.136
conducted extensive experiments to verify the impact the regularization loss coefficient ju on training, shown in Table [1] Here, 0 indicates that no regularization penalty is applied in the first stage, and the second Tearnable scalar du is directly removed at the beginning of the second stage. The results demonstrate that the transition process using the regularization strategy leads to better optimization outcomes for the binarized DM. Furthermore, EBB shows good robustness to μ. with moderately larger y yielding better final generative performance.
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Table 10: The impact of EBB application scopes on -eduooos (2/2).
Head and Tail Parts
Central Parts
#Bits
FID
sFID
Precision
Recall
1/32
8.02
12.81
64.83
33.12
0
1/32
7.20
12.27
65.62
34.98
1/32
6.99
12.15
67.51
36.80
0
1/32
7.10
12.22
65,41
36.42
12
1/32
7.10
12.29
66.41
34.54
Table 11: The impact of the regularization loss coefficient, on L.UN- 256 x 256.
#Bits
FID.
sFID
Prec.t
Recall
0 1/32
8.01
13.16
64.34
30.06
9e-2
I/32
6.99
12.15
67.51
36.80
9c-3
1/32
7.26
12.26
65.10
34.44
9e-4
1/32
7.18
11.83
66.96
34.54
We conducted experiments on the timing of EBB's transition to the second stage. In Table 12 an iteration of 0 indicates that EBB is not applied. The results demonstrate the effectiveness of EBB and the transition strategy with regularization penalties, with a slightly longer regularization phase yielding marginally better final generative outcomes for binarized DMs.
Table 12: The impact of the iteration which EBB transitions to the second stage LSUN- Bedrooms 256 x 256.
Iterations
#Bits
FID.
sFID
Prec.
Recall
0
1/32
8.22
13.02
61.45
32.88
10000
1/32
7.08
12.30
64.99
36.18
100000
1/32
6.99
12.15
67.51
36.80
Further Discussion of EBB. From the perspective of the final optimization outcome, in Eq removing the sign function from the second term-i.e., replacing on sign (w- 0₁ sign (w)) with ou (w Ti sign (wa)-can also achieve the same final evolutionary state. However, although this modification may provide stronger fitting ability in the early stages, it not beneficial achieve fully binarized final model through optimization. This is because it would lead to significant imbalance between the representations of the initial and final stages, causing the second term corresponding to on to dominate due to its excessive information extraction capability, which in turn hinders the subsequent optimization of 01 sign (w).
The additional experimental results we present in the Table 13 show that this idea did not achieve the optimal generation performance. At the same time, we observed the value of on the end of the first phase of EBB training. We found that, unlike the original approach where regularization would force converge nearly zero, dn still had a relatively large value, which indicates that this idea indeed hindered the natural evolution from multiple bases to a single base, and reduced the effectiveness of EBB as a method designed to enhance learning ability.
Table 13: The impact of applying the sign function to the second term EBB on 256 x 256.
Method
#Bits
FIDJ
sFID
Prec.t
Recall
Baseline
1/4
10.87
15.46
64.05
26.50
no sign in second term
1/4
8.44
13.00
62.68
30.12
BinaryDM
1/4
7.74
10.80
64.71
32.98
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Effeets of LRM. As supplement to the ablation study the final generation performance (Table in the main text, we present in Table 14 the changes in training loss (Asimple) at different iterations. The results indicate that LRM consistently achieves lower training loss, demonstrating its benefits for convergence.
Table 14: Training loss (impple) different iterations on L.UN-Bedrooms, comparing the no distilation, MSE and the addition of LRM.
Iterations
Method
#Bits
1el
1e2
1e3
le4
1e5
Baseline
1/32
0.388
0,303
0.277
0.227
0.158
LMSE
1/32
0.388
0.303
0.277
0.227
0.158
LLRM
1/32
0.352
0.264
0.242
0.206
0.151
We evaluate the performance of our binarized diffusion model under various values of K (reduction times of dimension) when incorporating LRM. Additionally, we compare these results with the outcomes of applying MSE distillation directly to the output features of blocks without dimensionality reduction. The experiments reveal the model's generation capability improves effectively when an appropriate degree of dimension reduction is employed, illustrated in Table 15
Table 15: In the application of LRM, the impact of different reduction times of dimension on the 256 256.
experimental results on
Fdistil
K
#Bits
FID
sFID
Prec.t
Recallt
1/32
7.39
12.34
65.98
35.84
LmSs
1/32
7.36
12.76
62.05
33.64
2
1/32
7.21
12.22
65,86
36.00
LIRM
4
1/32
6.99
12.15
67.51
36.80
8
1/32
6.95
12.02
64.20
35.44
As additional clarification on stability, also conducted experiments where the dimensionality reduction matrix F. RJ is updated every 100 iterations. As shown in the Table 16 while using LRM consistently yields improvements (with FID decreasing from 7.39 to 7.1 7/11/6,9 the approach of initializing the matrix once and retaining it throughout results in the highest accuracy. This further confirms our analysis that fixing the dimensionality reduction matrix and not updating more beneficial for stable optimization.
Table 16: Results of different update frequency of LRM on LSUN-Bedrooms.
Update Frequency (/iter)
#Bits
FIDU
sFID
0 (w/ LRM)
1/32
7.39
12.34
100
1/32
7.11
12.23
(BianryDM)
1/32
6.99
12.15
Further Efficiency Analysis. We pointed out in the main text that certain high-order-bassee based structures computationally unfriendly. In fact, The models produced by method save 1.96x in parameters (Size) and 2.00x computational operations (OPs) during inference, and we have also provided hardware implementations. Specifically, methods based higher-order residual bases require more sets of binarized weights and corresponding scaling factors during inference compared to Baseline or BinaryDM (Eq 10):
(18) This at least doubles the parameter count and OPs. Additionally, although multiple sets of bases in higher-order methods expected to be processed in parallel during inference, found in research that, to date, there has not been any implementation of this, making them computationally less efficient.
J (w +o (w
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For actual hardware, implemented convolution and linear layers unit by unit to estimate the overall model, utilizzig the general deployment library Larq[ [] on Qualcomm Snapdragon 855 Plus to test the actual runtime efficiency of the aforementioned single convolution. Since the current deployment libraries do not support direct computation for W A4, we used combined approach to achieve it via W1A1. Specifically, for the A4 operator, since there is existing 4-bit activation implementation, we decompose the activation as follows:
k a Ahst 4k: bal 1bst 2k: do2 1bst
k. b
1bit
1 k Do1 +
1bst
1
(19)
2
where
k is the scaling factor of fp32 activation,
a thit E {-88 -7, 6, -5, -, 2, -,,2,,11,
boi 1bit E {-1,1)) (1.2.3.4)
As result, the computation of 1-bit weights with int4 can be straightforwardly decomposed into the computation of 1-bit weights with 4 I-bit activations and one bias term k), based on the WIAI operator provided by Larq. with the addition of limited arithmetic operations. The runtime results for a single inference are summarized the Table 17 Due to limitations the deployment library and hardware, Baseline/BinaryDMM achieved 4.62x speedup, while High-Orde only achieved an 3.11x speedup. With further hardware support for binary operations. BinaryDM is expected to achieve performance closer the theoretical OPs calculations (15.2x), further widening the gap between its implementation and that of high-order methods.
Table 17: The actual runtime efficiency of a single convolution.
Method
#Bits
Size(MB)
Theoretical OPs(x 10%)
Runiine(ussconvoluriin))
FP
32/32
1045.4
96.0
176371.0
High-Order
1/4
70.2
12.6
56657.5
BinaryDM
1/4
35.8
6.3
38174.2
B.3 VISUALIZZAION RESULTS
Visualization of the impact of LRM. As complement Figure 3 present the distance in output features between binary DM and full-precision DM on more blocks under different distillation losses. As shown in Figure our proposed PCA-based distillation strategy consistently possesses the optimal guiding constraint capability.
Additional Random Samples. We showcase random generation results various datasets, with unconditional generation on LSUN-Bedrooms, LSUN-Churches, and FFHQ datasets, and conditional generation ImageNet. Overall, BinaryDM exhibits the best generation performance across datasets and maintains relatively stable performance as the activation bit-width decreases from 32 to 4 bits. In contrast, the Baseline lacks detailed textures and experiences significant performance degradation as the activation bit- width decreases.
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Distillation
TimestepBlockk 01
TimestepBlock @
TimestpDlock 01
TimestepBlock 04
TimestepOlock 05
Timestep Block 06
2.29
3,00
139
11
3110
3.10
Apr
2.5
1.0
050
24
4/
3.0
140
04
040
0:38
1.50
1.5
TimosppBlockk77
TincstepSlocke11
TinckepSoocke12
3.0
200
E D-DDsttncce
0.40
140
450
Block-1
Timeetep Blnncee Blocke-14
Timestep Block-18
1.0
7.0
304
54
464
200
Eak
204
Blocks33
Blocskp
Tineslep
Toncstep
Block--2
1.4
4.50
2.0
1:2
2.50
2.50
70
2.0
040
0.00
Training Iteration
Figure 5: A comprehensive record of the impact of different distillation loss functions on the output features of each block both full-precision DM and binarized DM, measured using the La distance.
W4 Baseline
W1A4 BinaryDM
WIA8 Buseline
WIAS RinaryDM
W1A32 Baseline
WLA32 BinaryDM
Figure 6: Samples generated by BinaryDM and Baseline on LSUN-Bedrooms 256 x 256
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W1A4 Raseline
W1A4 RinaryDM
W1A8 Baseline
W1A8 BinaryDM
W1A32 Baseline
BinaryDM
Figure 7: Samples generated by BinaryDM and Baseline on FFHQ 256 x 256
W1A4 Baseline
W1A4 BinaryDM
Baseline
WIAS BinaryDM
W1A32 Baseline
W1A32 BinaryDM
Figure 8: Samples generated by BinaryDMM and Baseline LSUN-Churches 256 256
W1A4
W1A4 BinaryDM
WIAS Baseline
WIAS BinaryDM
W1A32 Baseline
W1A32 BinaryDM
Figure 9: Samples generated by BinaryDM and Baseline on ImageNet 256 x 256
22


Reviews:
[{"review_id": "XKKYFGjxr2", "reviewer": "Reviewer_F7Tj", "summary": "The paper introduces BinaryDM, a novel approach for accurate weight binarization of diffusion models (DMs) to achieve efficient deployment and inference on edge devices. The authors identify that binarizing DMs is challenging due to severe accuracy degradation caused by limited representational capacity and optimization difficulties. To address these issues, they propose two key techniques: 1)Evolvable-Basis Binarizer (EBB): This method enhances the initial representation capacity by starting with multiple binary bases and learnable scalars, which are gradually regularized to evolve into efficient single-basis binarization during training. EBB is selectively applied to crucial parts of the DM architecture to retain stability and reduce training overhead. 2)Low-rank Representation Mimicking (LRM): This technique improves the optimization process by aligning the low-rank representations of the binarized DM with those of a full-precision counterpart, mitigating the optimization direction ambiguity caused by fine-grained alignment. The authors conduct extensive experiments on various datasets and demonstrate that BinaryDM achieves significant accuracy improvements over state-of-the-art quantization methods under ultra-low bit-widths, while also providing substantial efficiency gains in terms of model size and computational operations.", "questions": "1. Can the authors provide more justification for the selective application of EBB to only the first and last six layers of the DM architecture? How critical is this choice, and how does it affect performance and training stability?\n2. While the paper focuses on diffusion models, are there other binarization methods from other domains (e.g., binarized neural networks in classification tasks) that could be adapted for DMs? How does BinaryDM compare with such methods?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper addresses the challenging problem of binarizing diffusion models. The proposed methods, EBB and LRM, are novel and tailored to address specific issues in binarizing DMs.\n2. The authors provide a thorough experimental evaluation of their methods across multiple datasets and models. The results demonstrate that BinaryDM outperforms existing quantization methods under ultra-low bit-width settings, validating the effectiveness of the proposed techniques.\n3. The paper is generally well-written and organized. The motivation behind the proposed methods is clearly explained, and the technical details are presented with sufficient depth. Figures and tables effectively illustrate the concepts and results.\n4. Achieving efficient and accurate binarization of DMs is important for deploying these models on resource-constrained devices. The substantial efficiency gains demonstrated by BinaryDM highlight its potential impact in practical applications.", "weaknesses": "1. The Evolvable-Basis Binarizer (EBB) is selectively applied only to the first and last six layers of the diffusion model, covering only a small portion of the total parameters. This limited application scope raises concerns regarding the method’s generality and effectiveness throughout the network. Although the paper suggests that these head and tail layers are critical and parameter-sparse, it lacks a thorough justification or empirical evidence for this choice. Additionally, the middle layers, which remain untouched by EBB, may contribute significantly to the model’s performance and could also benefit from the method. By limiting EBB to specific layers, the paper potentially misses opportunities to enhance the representational capacity of the entire network. A more comprehensive exploration of applying EBB across different layers, including ablation studies, could provide insights into its most effective usage.\n2. The paper introduces the Evolvable-Basis Binarizer (EBB) and Low-rank Representation Mimicking (LRM) to address challenges in training binarized diffusion models. However, it lacks a thorough analysis of training stability and convergence behavior. Binarized models are notoriously difficult to optimize due to the discrete nature of weights and activations, which can lead to issues like gradient mismatch and convergence to poor local minima. The paper would benefit from a detailed investigation into how EBB and LRM specifically improve training dynamics.\n3. The paper compares BinaryDM primarily with baseline binarization methods and some low-bit quantization techniques like LSQ and Q-Diffusion. However, it does not thoroughly benchmark against the latest state-of-the-art quantization and binarization methods specifically designed for diffusion models or other generative models. Recent advances might offer competitive performance. A more comprehensive comparison would provide a clearer picture of where BinaryDM stands.\n4. The paper focuses on empirical results but lacks a theoretical analysis of why the proposed methods improve performance. Providing theoretical insights or analysis could enhance the understanding of the underlying mechanisms.\n5. Some technical details, particularly in the description of LRM and the training procedure, could be elaborated further to improve clarity. For instance, the choice of hyperparameters, how the low-rank projection matrices are computed and fixed, and the stability considerations during training.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "kcgXiSDUN3", "reviewer": "Reviewer_A5R1", "summary": "This paper introduces BinaryDM achieving weight binarization in diffusion models while mitigating accuracy degradation. BinaryDM tackles the challenges of information loss and optimization difficulties inherent in binarization through two key techniques: Evolvable-Basis Binarizer (EBB) and Low-rank Representation Mimicking (LRM). EBB employs a multi-basis structure during training, allowing for a smooth transition to a single-basis binary representation for inference, thus enhancing representational capacity. LRM, on the other hand, facilitates the stable convergence of binarized DMs by mimicking the representations of a full-precision counterpart in a low-rank space, addressing the optimization direction ambiguity caused by extreme discretization.", "questions": "1. While BinaryDM shows good result in diffusion models, there are many works that prove good result on other models like ReActNet [1] and InstaBNN [2] (There are much more existing works). Since there are not many existing works in diffusion model quantization, the results in this paper is not enough to prove the true superiority of BinaryDM.\n2. On the Evolvable Basis Binarizer (Equation 5), is there any reason the authors used “\\sigma_{II} sign(w - \\sigma_1 sign(w))” instead of “\\sigma_{II} (w - \\sigma_1 sign(w))” in second term? In this reviewer’s intuitive thinking, not utilizing sign function in second term would give more favorable initial state.\n3. Details: Are the number of training iterations of BinaryDM and existing works same? Also curious if the learning rate or schedulers are used same as in existing works.\n\n[1] Zechun Liu, Zhiqiang Shen, Marios Savvides, and Kwang-Ting Cheng. Reactnet: Towards precise binary neural network with generalized activation functions. ECCV, 2020\n\n[2] Changhun Lee, Hyungjun Kim, Eunhyeok Park, and Jae-Joon Kim, INSTA-BNN: Binary Neural Network with INSTAnce-aware Threshold, ICCV, 2023", "limitations": "", "rating": 8, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Existing binarization works benefit a lot from exploiting residual connections which holds full precision information in the connection it self without information loss. This method exploit this benefit to the initial state of binarization to start with good initial state for lowering accuracy degradation without changing any network structure in the final state.\n2. BinaryDM demonstrates superior accuracy and efficiency compared to existing binarization and low-bit quantization methods.", "weaknesses": "Please see the questions below.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "VDO2KKMLgh", "reviewer": "Reviewer_riMU", "summary": "In this work, the authors propose a quantization-aware training method that targets ultra-low bit-width representations, down to 1 bit resolution, oriented to diffusion models. More specifically, the proposed method consists of two parts, one focused on the feature representation of the applied diffusion architecture and the other on the optimization process. From the representation perspective, the authors propose a novel mechanism that gradually reduces the bases of binarized weights from higher to single-order base, applying a regularization term that according to the authors allows to smoothen the binarization process offering rich representation during the initial stage of training. Furthermore, the authors introduce a binarization-aware optimization method that projects the binarized and full-precision representations to lower ranks, applying Principal Component Analysis, forcing the low-rank binary representation to mimic the full precision one. This, according to the authors, enables the optimization of binarized diffusion models to focus on the principal direction and mitigate the ambiguity of the direction caused by the representation complexity of generation. The proposed method is applied in supplement with the vanilla binarization, with the proposed method targeting the most sensitive modules of the architecture, meaning on the outer layers, with the vanilla binarization applied on the intermediate layers. The paper provides extensive experimental evaluation on various datasets, including ablation studies, showing the effectiveness of the proposed method in contrast to the applied baselines, with the authors claiming that the applied methodology can significantly reduce the required Point Operations during the inference.", "questions": "The authors mention that the existing works have enhanced the binarized parameters via higher-order residual bases, but they introduce additional hardware complexity. However, the paper does not provide any evidence that the proposed method can be actually deployed in hardware accelerators without additional hardware, while the efficiency analysis reported is based on an estimation of OPs. The authors should note on the efficiency analysis section of the paper that is based on estimation and it would be beneficial to further discuss how their proposed method benefits the hardware inference in contrast to the existing methodologies. Can the authors elaborate on that, what overhead is introduced in existing methods in contrast to the proposed one?\n\nWithout theoretical nor empirical analysis regarding the location selection, I am concerned about how the authors conclude on applying the proposed approach on the first and last six layers of the models. Does the proposed method can be applied out-of-the-box on other architectures without applying exhaustive search on which layers should be applied? This makes me even more concerned regarding the generality of the proposed method is the fact that the proposed method is computationally intensive since it applies quantization-aware training that requires the computation of the covariance matrix of the binarized and full-precision representation. This introduces significant limitations on searching the layers where the application of the proposed method could be beneficial, hindering its generalization ability.\n\nThe notation used in some cases is weak. For example, it is not clear whether Equation 6 is applied channel-wise. Additionally, in the case of the trainable parameter $\\sigma_{1}$ the domain is missing, raising the question whether the sigma can change the polarity of the binarized parameter or not. Additionally, it is not clear in the text if the $\\sigma_{1}$ parameter is discarded after the training or if it is used also during the inference. Furthermore, using the same notation to denote different parameters as in the cases of Equations 9 and 2 can be misleading. Finally, $\\epsilon_t$ is not properly defined in the text.\n\nAlthough the most interesting part of the proposed method is the effective bit reduction down to 1W4A, the ablation study, which evaluates the different parts of the proposed method, is conducted only for 1W32A. I strongly recommend the authors to also include an ablation study for 1W4A, as it is the most impressive achievement of the proposed method.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "The proposed method results in significantly lower sized models with improved performance in reference to the baselines. This can potentially lead to significantly lower point operations and memory size during hardware deployment.\n\nThe proposed Evolvable-Basis Binarized results in richer representation during the initial stage of training as reported in Figure 2, showing significantly higher variance of parameters during the first iterations. As far I can say, the proposed method in fact smoothen the optimization process.\n\nIn general, the proposed method achieves sufficient performance in the challenging task of binarization.", "weaknesses": "The authors mention that the existing works have enhanced the binarized parameters via higher-order residual bases, but they introduce additional hardware complexity. However, the paper does not provide any evidence that the proposed method can be actually deployed in hardware accelerators without additional hardware, while the efficiency analysis reported is based on an estimation of OPs. The authors should note on the efficiency analysis section of the paper that is based on estimation and it would be beneficial to further discuss how their proposed method benefits the hardware inference in contrast to the existing methodologies. Can the authors elaborate on that, what overhead is introduced in existing methods in contrast to the proposed one?\n\nWithout theoretical nor empirical analysis regarding the location selection, I am concerned about how the authors conclude on applying the proposed approach on the first and last six layers of the models. Does the proposed method can be applied out-of-the-box on other architectures without applying exhaustive search on which layers should be applied? This makes me even more concerned regarding the generality of the proposed method is the fact that the proposed method is computationally intensive since it applies quantization-aware training that requires the computation of the covariance matrix of the binarized and full-precision representation. This introduces significant limitations on searching the layers where the application of the proposed method could be beneficial, hindering its generalization ability.\n\nThe notation used in some cases is weak. For example, it is not clear whether Equation 6 is applied channel-wise. Additionally, in the case of the trainable parameter $\\sigma_{1}$ the domain is missing, raising the question whether the sigma can change the polarity of the binarized parameter or not. Additionally, it is not clear in the text if the $\\sigma_{1}$ parameter is discarded after the training or if it is used also during the inference. Furthermore, using the same notation to denote different parameters as in the cases of Equations 9 and 2 can be misleading. Finally, $\\epsilon_t$ is not properly defined in the text.\n\nAlthough the most interesting part of the proposed method is the effective bit reduction down to 1W4A, the ablation study, which evaluates the different parts of the proposed method, is conducted only for 1W32A. I strongly recommend the authors to also include an ablation study for 1W4A, as it is the most impressive achievement of the proposed method.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)