AccuQuant: Simulating Multiple Denoising Steps for Quantizing Diffusion Models
Authors: Seunghoon Lee
Jeongwoo Choi
Byunggwan Son
Jaehyeon Moon
Jeimin Jeon
Bumsub Ham
Venue: NeurIPS 2025 poster ()
Keywords: Network Quantization
Diffusion Models
Primary area: applications

Abstract: We present in this paper a novel post-training quantization (PTQ) method, dubbed AccuQuant, for diffusion models. We show analytically and empirically that quantization errors for diffusion models are accumulated over denoising steps in a sampling process. To alleviate the error accumulation problem, AccuQuant minimizes the discrepancies between outputs of a full-precision diffusion model and its quantized version within a couple of denoising steps. That is, it simulates multiple denoising steps of a diffusion sampling process explicitly for quantization, accounting the accumulated errors over multiple denoising steps, which is in contrast to previous approaches to imitating a training process of diffusion models, namely, minimizing the discrepancies independently for each step. We also present an efficient implementation technique for AccuQuant, together with a novel objective, which reduces a memory complexity significantly from $\mathcal{O}(n)$ to $\mathcal{O}(1)$, where $n$ is the number of denoising steps. We demonstrate the efficacy and efficiency of AccuQuant across various tasks and diffusion models on standard benchmarks.

AccuQuant: Simulating Multiple Denoising Steps for Quantizing Diffusion Models
Scunghoon Lee"
Jeongwoo Choi"
Byunggwan Son
Jachyeon Moon
Jeimin Jcon
Bumsub Ham
School of Electrical and Electronic Engineering, Yonsei University
https://cvlla.yoosss htt.://sss....../p/pprretsccuuua
Abstract
We present in this paper a novel post-traiming quantization (PTQ) method, dubbed AccuQuant, for diffusion models. We show analytically and empirically that quan- tization errors for diffusion models are accumulated over denoising steps in a sampling process. To alleviate the error accumulation problem, AccuQuant mini- mizes the discrepancies between outputs a full- cull-precision diffusion model and its quantized version within a couple of denoising steps. That it simulates multiple denoising steps of a diffusion sampling process explicitly for quantization, account- ing the accumulated errors over multiple denoising steps, which is in contrast previous approaches to imitating training process of diffusion models, namely, minimizing the discrepancies independently for each step. We also present an efficient implementation technique for AccuQuant, together with novel objective, which reduces memory complexity significantly from
(n) to O(1), where n is the number of denoising steps. We demonstrate the efficacy and efficiency of AccuQuant across various tasks and diffusion models on standard benchmarks.
Introduction
Diffusion models [17, 49] have shown the effectiveness for various generation tasks, including text- to-image generation [41, 43], audio generation [29], and video generation [2, 1, 12). In the context of image generation, diffusion models train neural networks denoise images progressively, corrupted by Gaussian noise, reversing the noisc-adding process, and recovering original images. At test time, starting from random noise, diffiusion models perform a sampling process, where the trained neural networks denoise the corrupted image gradually. To generate realistic images, the sampling process typically involves lots denoising steps, which is computationally demanding. To overcome this problem, many approaches attempt reduce the number of denoising steps [35, [35,55], 55], providing efficient image generation process. Another line of research focuses on compressing neural networks themselves (e.g., using network quantization [25, 19] pruning [4]) to reduce the computational cost for each denoising step.
Network quantization lowers bit-widths of full-precision weights and activations into lower ones, enabling a fixed-point computation for efficient inference. There are mainly two approaches to quantizing neural networks: Quantization QAT optimizes network weights and quantization parameters (e.g.. step-sizes and zero-points) jointly using entire training samples, which is computationally expensive, making it hard apply QAT for large models (e.g., ViTs [8]). PTQ has recently gained significant attention across various models [37, 26, 34, 36] due to its efficiency. In contrast to QAT, PTQ calibrates quantization parameters only without retraining the network weights, using a small subset training samples.
training (QAT) and post-training quantization (PTQ).
Equul contribution. Cooresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Noise
..
Previous approaches
AccuQuent
F0
Xx-1
X1
Xx-1
Xp-2
Xe-2002
Xe-Mt
EaccoOum!
Sampling
aingle dencising slep
Denolding
Gradeet
8--1
mpprommation
9/-1
8--2
P2-1241
Previous methods minimize the quantization error at each denoising step individually, failing account for accumulated quantization errors during calibration. Right: AccuQuant addresses this problem effectively and effi- ciently by simulating multiple denoising steps of diffusion models, that is, aligning generated images of full-precision and quantized models over multiple denoising steps, with a memory complexity of (1), independent of the number of steps.
Figure 1: Calibration processes of previous approaches and AccuQuant. Left:
Albeit efficient, challenging to directly apply PTQ methods, designed for neural networks for discriminative tasks, such image classification, diffusion models, since they involve sequential process to denoise images. As the sampling process goes on, the quantization error at each denoising step propagated. An overall quantization error can then be split into two parts: Quantization error at the current denoising step and the error accumulated along the previous steps. Most methods [45, 25, 48, 19] neglect the accumulated error, and try to minimize the quantization eтror at each denoising step (Fig. ((eeft).. Specifically, they exploit the same error-free image as inputs at every step for both full-precision and quantized models, while not considering that the input of the quantized model could contain quantization error accumulated along previous sampling steps. They then calibrate quantization parameters to minimize the difference between the outputs of these models at every step. This is not enough to reduce the overall quantization error, resulting in substantial performance degradation. Although recent works attempt to address the accumulated errors, they are able to handle single-step errors only [50] or require additional parameters for error correction [54, 14].
We introduce in this paper a novel PTQ method for diffusion models, dubbed AccuQuant, that minimizes an overall quantization error, including the ones accumulated over previous denoising steps effectively and efficiently (Fig. 1(igght).. To this end, AccuQuant groups a couple of denoising steps, and minimizes the difference between the outputs of quantized and full-precision models for each group to calibrate quantization parameters. That is, AccuQuant considers multiple denoising steps in the diffusion process, in contrast to previous approaches to simulating single denoising step only [25, 14, 48, 19], namely, calibrating each step independently. This enables considering the accumulated quantization errors explicitly within each group to minimize an overall quantization error. A naive implementation of AccuQuant, however, requires substantial memory storing intermediate activations for all denoising steps within each group in order to compute gradients, resulting in memory complexity of O(n) w.r.t the number of denoising steps in each group. To address this, we propose a novel gradient approximation technique, together with a new objective, that reduces the memory complexity significantly from Onn) to ((1), enabling applying AccuQuant to large-scale diffusion models efficiently. We show that our approach achieves state-of- -tate-of-the-att the-art performance across various settings, especially in terms of FID2FP32 [50], which evaluates how closely the outputs of the quantized model match those of the full- full-precision model. This suggest that AccuQuant aligns the quantized model with its full- full-precision counterpart more effectively than previous methods [25, 48, 19, 14, 50].
We summarize the main contributions as follows:
We introduce a novel calibration method for quantizing diffusion models that aligns multiple denoising steps in the sampling processes quantized and full-precision diffusion models, reducing accumulated quantization errors effectively.

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We present a gradient approximation technique for an efficient inplementation of AccuQuant, together with a new objective, reducing the memory complexity significantly (1). We also provide detailed analysis on quantization errors of diffusion models.
We demonstrate the effectiveness of AccuQuant through extensive experiments across various models on standard benchmarks [16, 50, 15,59, 59, 38, 44].
2 Related work
2.1 Quantization for neural networks
Network quantization reduces the bit-width of weights and/or activations in neural network. QAT methods [5, 53, 24, 21] simulate the quantization process at training time by converting the full- precision weights/acttivtiinn into lower-precision representations through rounding function. This requires retraining the neural network quantize, which is computationally expensive. On the other hand, PTQ calibrates quantization parameters only with small number of calibration samples. quantizes neural networks efficiently, without involving a retraining process, but it is limited to handle outliers in weights/activations. This problem can be alleviated by clipping the outliers, adopting a outlier channel splitting technique [60]. or assigning different quantization step sizes for weights/activations with large magnitudes [3, 9J. Recent PTQ methods have demonstrated the effectiveness across various architectures, including CNNs [30, 46, 20J and transformers [57, 27, 36]. In particular, they optimize a rounding function for network weights (i.e., determining each weight to be rounded up or down), by exploiting the output differences of each layer [37, or a Hessian- based reconstruction metric [26], before and after quantization.
2.2 Quantization for diffusion models
Most approaches to quantizing diffusion models adopt PTQ technique, mainly due to its efficiency. Architectural characteristics of diffusion models make it difficult to directly apply existing PTQ methods, especially for extremely low bit levels. In particular, Q-Diffusion [25] shows that residual connections in diffusion models, such as U-Net [42], cause significantly different distributions for concatenated activations, and introduces a split guantization technique that performs quantization prior to the concatenation. TFMQ-DM [19] shows that previous PTQ methods, which are not designed for diffusion models, could disturb temporal features along denoising steps from original ones, and proposes to quantize temporal embedding layers of diffusion models separately.
Diffusion models apply denoising operation iteratively over time steps generate images, providing different distributions of activations across the denoising steps. In order to consider the time-varying characteristics of diffusion models for quantization, training samples in calibration datasets would be carefully chosen. To this end, Q-Diffusion [25] proposes to sample images uniformly along denoising steps. PTQ4DM [45] exploits a skewed normal distribution to sample more images later denoising steps, which typically provide more realistic images.
Related to ours, PTQD [14], TAC [54] and PCR [50] attempt to alleviate the effect of accumulated quantization errors. PTQD [14] and TAC [54] analyze the relationship between the outputs of a full- precision network and its quantized counterpart. Assuming that the outputs from these networks are related at each demoising step, they correct the accumulated errors by computing the correlation
coefficient and bias [14] or the reconstruction coefficient and bias [54]. However, these approaches require additional memory to store these parameters for each denoising setp, and incur computational overhead for the error-correction stage. PCR [50] instead tries reduce the accumulated quantization error directly in a calibration phase. Similar to ours, PCR [50] calibrates quantized diffusion model each denoising step progressively, but it exploits the generated image of quantized model in a previous step as inputs for both full-precision and quantized models. This could not account for the differences between quantized and full-precision models across multiple denoising steps effectively, mitigating quantization errors within single denoising step only. On the contrary, our approach exploits separate inputs for frel-precision and quantized models. That is, the inputs for full- preciireniionn and quantized models come from the corresponding models in previous denoising step, respectively. This enables minimizing the discrepancies between the quantized and full full-precision models across multiple denoising steps, reducing accumulated quantization errors explicitly. Although a memory complexity of our approach is O(n) w.r.t. the number of denoising steps, we provide an efficient alternative with a complexity of (().
3

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3 Method
In this section, we briefly describe diffusion models and network quantization (Sec.3.1). We then provide an analysis on quantization error in detail (Sec.3.2). Finally, we present a detailed description of AccuQuant, including a gradient approximation technique (Sec.3.3).
3.1 Preliminaries
Diffusion models. During forward diffusion process, Gaussian noise e, sampled from a normal distribution (0, 1), is added to input image To progressively time steps. Specifically, noisy image xy at step can be represented as follows:
Tt Vari0 VI- e~ I0,
(I)
where Ot is noise scheduling coefficient at the denoising step t. Diffusion models reverse this process, gradually removing the noise from the noisy image 2; to recover the original one 2o. To this end, neural network estimates and removes the noise from the corrupted image 2; iteratively, until a clean image is obtained. For example, for deterministic sampling of the DDIM sampler [49], sampled image of 2t-1 step f is computed as:
ltt
(t- + (1--01110(
01
where we denote by eø se( t) the noise predicted by the neural network, parameterized by 0, for the image 2, at step t.
Network quantization. Given a floating-poii value v and target bit-width 6, network quantization converts the value into low-precision integer T as follows:
clip rroudd (-)
0, 2 -1).
where we denote by and a step-size and zero- pero-poiit, respectively. round(-) is rounding function (e.g., nearest rounding or adaptive rounding [37, 26]), and clip(,, Umin Umax) is a clipping function that maps input value within range of [Umin, Umax]- The integer value ö is then re-scaled to obtain quantized value as follows:
i = s 2).
(4)
Note that the quantization parameters and z are trained with all training samples for QAT, while they are computed using small set of calibration samples for PTQ.
3.2 Quantization errors for diffusion models
In this section, we show that quantized diffusion models suffer from an eπror accumulation problem, where quantization error at each step is accumulated along the sampling process progressively, degrading the quality of generated images.
Let us denote by x; and cg an image and an estimated noise at the denoising step for a full-precision model, respectively. We define 3, and ég similarly for a quantized diffusion model. We first categorize the overall quantization error into two parts: a step error ó, representing the quantization error for the estimated noise ép at step and accumulated error A, representing the accumulated quantization error for the image T along all the previous steps. We can then represent ã and Eg as follows:
5, 24 + A., E0 1) = c (ze, 1) 6z-
(5)
(6)
By plugging Eqs. (5) and (6) into Eq. (2), we can compute the output image 5.-1 of the quantized model at step of - 1 as follows:
Je- = xz-1 + cgd. + d,Dr.
where
V 0t
C4:
Van-i
C
+ v 04-1, d,
(8)
13
Vog

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Xogmtuue at arror
Stop urroe Accumulated erroe
30-
Q-Difusioc
20-
Denotising
Denotising
stop
(a) Quantization errors on CIFAR-IO [23].
(b) FID2FP32 [50] comparisons on CIFAR-10 [23].
Figure 2: (a) We show the magnitude of the step error CDd, and the accumulated error de A, each denoising step. The accumulated error increases drastically, while the step error remains relatively constant, suggesting that reducing the accumulated error is crucial for generating better images, compared to the step error. (b) Q- O-Diffusion accumulates quantization errors according to denoising steps, resulting very high FID2FP32 score. On the contrary, our method effectively mitigates the problem, maintaining low score.
We show in Fig. 2a the step error of c₁d, and the accumulated error of d, ; in Eq. (7) at each denoising step of DDIM [49] on CIFAR-10 [23]. Specifically, assume that 6; is Gaussian noise with zero mean and unit variance, and calculate the accumulated error A recursively, Le.. A = c₁ó; d, A. starting from Ar being O, where T is total number of denoising steps. We can that the accumulated error d, increases drastically according to denoising steps, while the step error c, does not. This suggests that the accumulated error for the image ã; have much greater impact on the quality of a generated image, compared with the step error for the estimated noise, as the sampling process goes on.
To further validate our observation, we simulate in Fig. 2b the sampling process of DDIM [49] with Q- Diffusion [25]. and compute FID2FP32 [50] with generated images from full-precision and quantized models at every steps. Note that FID2FP32 [50] measures the FID score [16] with the outputs of quantized and full-precision models, evaluating how closely the quantized model approximates the output from its full full-precision counterpart. We can see from the blue line in Fig. 2b that FID2FP32 [50] increases accordingly along denoising steps, demonstrating once again that quantization errors accumulated in the sampling process. Note that all diffusion models, generating images through multiple denoising steps, suffer from the error accumulation, similar DDIM [49] in Fig. 2b, regardless types of sampling methods. Therefore, reducing the accumulated error would be key to maintain the quality of generated images for quantized diffusion models.
3.3 AccuQuant
To address the error accumulation problem, we introduce a novel PTQ method for quantizing diffusion models, dubbed AccuQuant, that imitates multiple denoising steps of full-precision diffusion model, reducing the accumulated error effectively. Unlike previous approaches to focusing on individual denoising steps [45, 25, 48, 19, 54], our framework simulates the multiple denoising steps in sampling process of full- full-precision diffusion model for quantization. This enables considering the accumulated error during calibration process (i.e., optimizing quantization parameters), reducing the error for quantizing diffusion models.
Specifically, we group M consecutive denoising steps, splitting entire denoising sequence into total of T/M groups. That is, a denoising step for the 1th group starts with step of T M( 1). Given an image obtained from the full-precision model at step I, denoted by st, apply denoising process M times to generate images of Tx- Ms and T.- as from full-precision and quantized models, respectively, follows:
Mt-M = DM (),,t), ēt-M =
where Da represents a denoising process for the full-precision model over M steps. DM is defined similarly for the quantized model with the step size of s; for quantization. To calibrate the step-size for the th group, we minimize the mean squared error between z,-M and ã,-M as follows:
arg min LMSE(II, s1))
(10)
where
CMSE(2 st:) Da (z,, t) Das (2 8i) $
(11)
5

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The calibration process is then repeated sequentially for each group. By doing so, AccuQuant accounts for the overall quantization error (i.e., both quantization errors at individual steps and accumulated ones within multiple steps), without introducing additional parameters or extra computational costs during sampling process.
order to com- pute gradients for calibrating quantization pa- rameters, AccuQuant requires lots of memory to store feature maps for all denoising steps within group. For the nt group, the gradient of the ob- jective LMSE w.r.t. the step-size s; is computed as follows:
Gradient approximation.
Grodient Moquitude
3.0
0.2
1000
LLMSE Usi
0LMSE
Denoising
DT.-M
Us:
Figure 3: Plots of the gradient in Eq. (14) and its components over denoising steps. The gradients (12) are calculated during calibration process of Ac- cuQuant for DDIM [49] on CIFAR-I0 [23]. Shade indicates the standard deviation.
a m
Σ Im
0ū.-M M
0s:
Lmm=1
where Im is a cumulative product of partial derivatives, across multiple denoising steps, between input and output images, follows:
m M
Im I
08.-M-141
0B--M+3
m
M.
(13)
This suggests that should store all intermediate feature maps, calculated across denoising steps within each group. to compute 9m. This results in memory complexity of O(M) w.r.t. the number of denoising steps, which limits the scalability of AccuQuant.
To address this, we propose an efficient implementation technique to reduce the memory complexity. We represent the gradient between consecutive denoising steps for the quantized diffusion model as follows:
0 van-i
0ā.-1
Deo (Te, 1)
I Ct
(14)
0E. Vos
0E:
We have empirically observed in Fig. that the first term in Eq. (14) dominates the entire gradient, whereas the second one is negligible (see red and blue lines). Similar findings are reported in [40, 58]. Based on this observation, we approximate the gradient in Eq. (14):
08,-1
I.
(15)
az,
VaL
Using the approximation in Eq. (15), we can represent Im in Eq. (13) as:
2 VaL-M 1, for m = 1,2, .,, M.
(16)
Var-m
That is, can simplify the gradient, computed by backpropagating through multiple denoising steps, into a scalar ratio of noise scheduling coefficients, reducing the memory complexity from (MM) to O(1). Using the approximation in Eq. (16), the gradient of the objective in Eq. (12) can then be represented as follows:
LMME ds:
OLMSE
Va--M M 08
(17)
dū.-M M
at--
ds:
To fully exploit the approximated gradient of Eq. (17), we introduce new loss function:
M
Q M
LAceuquant
5g(2;- - f(-M) + Zt-m - -g( 1|
(18)
m=1
m
such that its gradient becomes Eq. (17). Here, sg is groddira operator preventing computing gradients. Accordingly, we calibrate the quantization parameters of quantized diffusion models by optimizing the objective of Eq. (18), while considering the accumulated errors with a memory complexity of O(1). Detailed derivations for Eqs. (16) and (18) and the algorithm of AccuQuant can be found in the section A.

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Table I: Quantization results for unconditional image generation on CIFAR- 10 (32 x 32) [23], LSUN- Churches (256 x 256) and SSUN-Bedrooms (256 x 256) [56]. f: The official implementation of TFMQ-DM uses a 32-bit for certain layers, such as attention modules. We modified these components, such that all layers are quantized with the same bit- bit-width, for fair comparisons with other methods. TAC [54] does not provide source codes, and thus its performance cannot be measured.
Model
Method
Bits(WA) 1S1 FID FID2FF32.
Model
Method
Bis(WA) FID. <FID.
FID2FF322
Full ProciPiciio
32/32
9.09
4.26
0.00
Full-Precision
10.10
Q-Dafusienn [25]
10.36
0.79
Q-Ditfusion [25]
8.63
30.46
35.24
TFMQ-DM [19]
48
3.43
19.85
10,14
TFMQ-DM [19]
3.64
TAC [54]
Ours
6/6
9.18
5.79
3.30
Ours
4/8
3.99
10.67
0.66
Q-Diffusion [25]
4/6
45.24
25.96
40.58
Q-Dilfosion [25]
9.12
3.26
TVMQ DM [19]
20.77
10.07
TEMQ-DM [19]
8,8
5.52
1.52
1.DM-8 LSUN Churches
Curs
TAC [54]
4/8
9.15
4.89
Q-Diffusion [25]
6868
Qurs
4/8
9.06
4.75
1.15
(steps=300)
TFMQ-DM [19]
3/08
9.03
21.77
10.48
TAC [54]
DDIM CIFAR-10
Q- Diffusion [25]
4/6
9:47
25.35
30.66
Ours
3/8
5.04
10.95
1.26
(Stepe=100) 100)
TRMQ-DM [1]
4/6
9.15
11.04
7.39
Q-Diftusion [25]
47.
27.97
42.27
Ours
4/6
X.99
7.07
3.94
TFMQ DM [19]
3/6
9:84
14,20
10.19
12.58
Diffussio [25]
3/8
8.53
17.31
13.94
TFMQ-DM [19]
3/8
8:40
28.47
26.96
Pull-Precision
7.077
TAC [54]
3/8
8.86
9.55
Q-Diffusion [25]
1.46
Ours
3/8
8.76
9.03
5.15
LDM-4
TAC [54]
TPMO-DM [19]
4/3
7.33
12,68
4,59
Q- Diiifuusion [25]
3/6
7,51
40.91
42.74
LSUN--Ediooe
Ours
(steps=200)
TFMQ-DM DM [19]
3/6
8.34
29.29
27.11
Q-Diffusion [25]
11.99
14.02
7.54
TFMQ-DMT [19]
3/0
11.32
11.62
7.64
8.27
31.88
TAC [54]
8.65
6.69
Ours
3/8
4.18
10.45
1.14
4
Experiments
We describe in this section implementation details (Sec.4.1), and compare our approach with other quantization methods quantitatively and qualitatively (Sec.4.2). We then present detailed analysis of our method (Sec.4.2). More quantitative and qualitative results can be found in the appendix.
4.1 Implementation details
Datasets and models. We apply AccuQuant to various diffusion models and perform extensive ex- periments on standard benchmarks for unconditional, plass-conditional, and text-to-imaae generation tasks. For the unconditional generation task, we exploit DDIM [49] on CIFAR-10 [23], and Latent Diffusion Model (LDM) [41] on LSSUN-edrromss and generation, we perform experiments using LDM [41] on ImageNet [6]. We use Stable Diffusion (SD) v1.4 [41] on MS-COCO [28] for exxt-to-image generation.
[56]. For class-conditional
Quantization. We employ adaptive rounding [37, 26] for weight quantizers, following prior approaches [45, 25, 19]. For activation quantization, split denoising process into 20 groups for unconditional image generation, 10 groups for class-conditional image generation and 25 groups for text-to-image generation. We perform the calibration process for 50, 20, and 10 epochs on DDIM [49], LDM, and SD [41], respectively, using the Adam optimizer [22]. Following the work of [25], we generate 256 calibration samples for each group with full-precision models, maintaining the total number of the samples consistent with that of [25] across all experiments. More detailed settings can be found in the section B.
Evaluation metrics. Following the previous approaches [25, 19, 54]. we evaluate 50K images for mmconditional/clas--coonii conditionn generation with Inception Score (IS) [44], Frechet Inception Distance (FID) [16], and sFID [38]. We also measure PSNR, SSIM, and LPIPS [59] between images generated by full-precision and quantized models for class-conditions image generation. For eext-to-image generation, we generate 5K images, and evaluate them with FID [16] and CLIP scores [15], following the work of [50]. The ViT-L/14 is used to compute CLIP scores [15]. We also
7

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Table 2: Quantization results for class-conditional image generation on ImageNet (256 256) [6].
Model
Method
Bits(W/))
FID
sFIDL
1S1
FID2FP32,
LPIPS!
PSNR
SSIM
Full- Precision
32/32
11.13
368.19
0.00
0.00
0.00
0.00
O-Diffusion [25]
4/8
9.55
13,50
339.44
1.71
0.1912
23.6703
0.8391
PTQD [14]
4/8
9.99
8.43
361.95
0.84
0.1598
24.0672
0.8614
TFMQ-DM [19]
4/8
9.80
7.19
358.38
1.25
0.1702
23.6309
0.8567
356.48
0.65
0.1585
0.8713
LDM-4
O-Diffusion [25]
3/8
7.57
12.43
266.65
11.26
0.3741
18.4588
0.6532
ImageNet
PTQD [14]
3/8
7.75
9.51
308.47
6,30
0.3446
19.2483
0.6728
(steps=20)
TFMQ-DM [19]
3/8
7.96
8.77
295.46
4.47
0.3942
16.8180
0.7200
Ours
6.61
8.65
301.06
3.86
0.2937
19,9392
0.7649
O-Diffusion [25]
3/6
28.83
39.30
99.55
41.25
0.4666
17.9855
0.6358
PTQD [1]]
3/6
9.15
11.42
244.43
13.85
0,3852
18.1508
0.6662
TFMQ-DM [19]
3/6
8.17
10.71
237.32
10.06
0.3928
17.4886
0.7183
Ours
5.95
8.61
282.87
6.31
0.3296
19.0135
0.729
Table 3: Quantization results for text-to-image generation on MS-COCO (512x512) [28]. MP: Mixed- precision quantization.
Model
Method
Bits(W/A)
FID
FID2FP32,
CLIP Score
Full-Precision
32/32
27.50
0.00
26.46
Stable Diffusion v1.4
O-Diffusion [25]
4/8
27.87
20.42
26.15
MS-COCO
PTQ4DM [45]
4/8
25.64
17.73
26.25
(steps=50)
PCR [50]
4/8.1 (MP)
23.86
14.39
26.35
PCR [50]
4/8.4 (MP)
22.04
14.25
26.48
Ours
4/8
22.73
10.99
26.85
use FID2FP32 [50] computing FID of generated images by quantized models, but with the images from full-precision models as a reference, measuring accumulated errors from quantized models for all experiments.
4.2 Results
Quantitative results. We show in Tables 1-3 quantitative comparisons of our method and the state of the art [25, 19, 54] for unconditional image generation (i.e., CIFAR-10 10 [23], ..SUN-Bedroom and LSUN-Churches [56]), class-conditional image generation (i.e., ImageNet [6]) and text-to-image generation (i.e. MS-COCO [28]), respectively. fair comparison, we report the results of TFMQ- DM [19], with official source codes provided by authors, under the same settings ours. We refer to the results from the papers for other methods that do not provide official implementations.
We summarize our findings as follows: (1) AccuQuant outperforms all previous approaches [45, 25, 14, 19, 54, 54], specially designed to quantize diffusion models, by significant margins in terms of FID2FP32 [50]. Specifically, it provides better results than PCR [50], even with lower bit-widths. This demonstrates that AccuQuant reduces accumulated errors effectively, and better maintains the behavior of full-precision models compared to other methods. (2) AccuQuant achieves significant performance gains, especially in low-bit settings for activation quantization. Note that low-bit settings are more vulnerable to accumulated errors, due to the limited representational capacity. This demonstrates the robustness of AccuQuant and its ability to maintain high performance, even under constrained conditions. (3) AccuQuant outperforms the state-of-the-e methods [25, 19, 54] in various standard benchmarks, verifying that considering multiple denoising steps in a sampling process is effective to reduce accumulated emrors for quantizing diffusion models.
Qualitative results. We provide in Fig. visual comparisons of generated images by full- precision model, Q-Diffusion [25], TFMQ-DM [19] and AccuQuant on LSUN-Bedrooms and LSUN-Churcher [56] for unconditional image generation. can see that AccuQuant provides more realistic images, and they are more close to the results from full-precision models, verifying once more that AccuQuant minimizes the discrepancies between full-precision and quantized models effectively. We also show Fig. 5 generated images, conditioned on text prompts, by SD v1.4 [41] and

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Full precision
Q Q-Diffusion [25]
TFMQ-DA [19]
Ours
Figure 4: Visual comparisons of generated images on (Top) LSUN-Bedrooms [56] and
(Bottom) [56] for unconditional image generation under a 3/8-bit biit setting.
Full-Precision
Q-Diffusion [25]
PCR (T = 0.20) [50]
Ours
Figure 5: Visual comparisons of generated images conditioned on text prompts. We generate
images by SD v1.4 [41] and its quantized versions using PCR [50] under a 4/8.4-bit setting and
Q-Diffusion [25], AccuQuant under 4/8-bit setting. denoising steps into 10 bits. The prompts corresponding to each column are: "A puppy wearing hat" and "A cute teddy bear in front of a plain wall, warm and brown fur."
0.20 indicates setting 20% of entire
its quantized versions using O-Diffusion [25], PCR [50] and AccuQuant MS-COCO [28]. We can observe that AccuQuant generates high-qualit, images that closely resemble those obtained by the -rreiiiin model, compared to Q-Diffusion [25] and PCR [50]. Note that PCR [50] exploits more bit-width: than ours, demonstrating the effectiveness of our approach to minimizing accumulated quantization errors. For example, the detailed shape of the hat, and the pose of the dog and teddy bear are preserved well for our method, while Q-Diffusion [25] and PCR [50] do not. More qualitative results can found in the appendix.
4.3 Discussion
Analysis group size. We compare in Table quantization results of AccuQuant, with different group sizes, for DDIM [49] on CIFAR-10 [23]. We can see that AccuQuant performs better accordingly with an increase of a group size from 1 to 5, con- firming once again that is effective for quantizing diffusion models to account for the behaviors full- precision and quantized models within multiple de- noising steps. This also suggests that considering accumulated errors
Table 4: Quantitative comparisons of Ac- cuQuant under a 6/6-bit setting with varying group size.
Group size
IS 1
FID 1
FID2FP32
1
9.17
6.96
5.62
2
9,02
6.82
4,48
5
9.18
5.79
3.30
10
9.13
6.18
4.30
enough with few denoising
8.69
14.52
14.19
steps. On the other hand, the quantization perfor- mance degrades, when the number of denoising steps is too large. This indicates that it is hard to estimate appropriate quantization parameters reducing the accumulated error across many denoising steps. To this end, the group size treated hyperparameter that balances two objectives: (1) sufficiently capturing accumulated errors across multiple timesteps, and (2) ensuring stable optimization of quantization parameters. As shown in Table 4, if the group size is too small. it may fail to capture the long term error accumulation; if it too large, the optimization becomes unstable as single set of parameters must account for diverse behaviors of many timesteps. The optimal group size can vary depending on the model and dataset, but we empirically found that dividing the timesteps into 10 20 groups yields consistently strong results across experiments.
100
7.86
50.11
57.96

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Table 5: Comparison of the full gradient
1) Jacobian 82t
Table 6: Quantitative comparisons of AccuQuant with and without gra- dient approximation. We quantize DDIM [49] on CIFAR-10 [23] with group size
term (ct Dig Deal (B..0) ), and our approximation. We quantize
DDIM [49] with CIFAR-I0 [23] under W4A8 settings and report the mean and the entire range the gradient at every 20 timestep.
Timestep
100
60
20
FID 4 /FID2FP32 +
Bits (WA)
1.0221
1.0586
1.0273
1,0082
1.0008
w/o Approx.
w/ Approx.
02r
#0.112
+00059
0.033
+0.034
++0001
6.13/4.02
5,79 3330
(ac.t)))
-0.1236
-0.0097
-0.0015
-0.0006
-0.0002
4/8
5.26/2.32
4.75 / 1.15
Cz dāe
#00112
+000559
0.034
+0.034
+-0.071
4/6
7.21/5.18
7.07 / 3,94
3/8
9.72/5.34
9.03 / 5.15
1.1457
1.0683
1.0288
1,0088
1.0010
10.26/7.80
9.89 6.69
Analysis of gradient approximation. We show in Table quantitative comparisons of AccuQuant with and without the gradient approximation technique. It shows that 1) AccuQuant with our gradient approximation technique even provides better results quantitatively, with much less memory, compared with those obtained without using the approximation, and 2) the performance gains are more significant for FID2FP32. This suggests that gradients of Eq. (14) are corrupted by substantial noise before the quantization parameters S of Eq. (10) converge, which makes the calibration process unstable. Specifically, better illustrate the variability of the gradients. As shown in the Table 5, Jacobian component (i.e., Row 2 in Table 5) is significantly smaller in average magnitude compared to the dominant scalar coefficient (i.e., Row Table 5), but it exhibits a high dynamic range that introduce substantial noise into the full gradient (i.e., Row in Table 5). This high-variance noise causes the quantization parameters to update inconsistently at each step, leading to an unstable and unreliable calibration process. In contrast, 3 in Table 5) by omitting the highly dynamic Jacobian term. This leads to more stable convergence during calibration and ultimately yields more optimal results, demonstrated in Table 6.
show in Table 5 the same statistics in Fig. 3 with the entire range to
gradient approximation exploit only the dominant scalar coefficient (i.e., Row
Limitation
AccuQuant requires multiple denoising steps during the calibration phase. While AccuQuant effec- tively mitigates accumulated errors and achieves strong performance even few-step settings such as 20 steps ImageNet [6], it may have limited efficacy when applied to diffusion models employing only 1-2 denoising steps [35, 55J. addition, AccuQuant has a hyperparameter, the group size, which is currently fixed across all groups. Exploring adaptive strategies to dynamically determine the optimal group size for each group would be an interesting direction for future work.
6 Conclusion
We have shown a detailed analysis on quantization errors of diffusion models that the errors are accumulated over denoising steps. Based on this, we have introduced novel PTQ method, dubbed AccuQuant, that alleviates the error accumulation problem by simulating multiple denoising steps in sampling process of diffusion model. We have also presented a gradient approximation technique to reduce the computational overhead of storing gradients for intermediate activations along the denoising steps. We have demonstrated that AccuQuant outperforms state-of-the-arr PTQ methods across various bit-widths on standard benchmarks.
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Acknowledgments and Disclosure of Funding
This work was supported by Institute of Information & Communications Technology Planning Evaluation (IITP) grants funded by the Korea government (MSIT) ment of Fundamental Technology and Integrated Solution for Intelligence System, No.RS- 2025-09942968, AI Semiconductor Innovation Lab(Yonse) University)), the National Research Foundation of Korea(NRE)) grants funded by the Korea governmen(( (No. 2023R A2C2004306, 14-2025-02216322 Samsung Electronics Co., Ltd (10240520-10013-01) and the Yonsei Signature Research Cluster Program of 2025 (2025-22-003).
Develop- Automatic Artificial
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NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: We introduce a quantization framework for diffusion models that reduces accumulated errors. We demonstrate the effectiveness of our framework on various bit- widths, model architectures, datasets, and baseline quantization methods.
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Answer: [Yes]
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We describe the limitations of AccuQuant the Appendix.
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Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
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Answer: [Yes]
Justification: We conduct a theoretical analysis of the accumulated quantization error in diffusion model quantization. We visualize the accumulated quantization error in Fig. 2a and Fig. 2b to validate our assumptions, and we also include the detailed derivation of AccuQuant in the Appendix.
Guidelines:
The answer NA means that the paper does not include theoretical results.
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A Detailed algorithm for AccuQuant
A.1 Algorithm table for AccuQuant
Algorithm Pseudo code of AccuQuant.
group size
# x_T random gaussian noise mo_model full-precisia model
quant model quantized model pather.outpute one iteration diffusion denoising step sg() stop gradient operation
Initialize x_t x
10
11 group indexindxxxxx =
for in
14
Gather (t-M) from Full Precision Model
15
with torch.no.grad..
fp_x_M gather-outppt((g (tt.ootttpptmmmmmme...t.... modellxxt,t
18
Reconstruction stage genn.mmoett.eet.grruugrgruu
19
20
aotimiize-ttrrch.pptim Adam(quant params, learning rate)
for epoch in range(epochs))
23
Gather Atilde (t-t- with stop gradient
24
with torch.no-grad():
sg-quant_x_M
x_m, quant_params)
27
optimizer..zerogrree
28
29
# Accumulate the gradient for in r
# Calculate gradient scaling factor
32
g.m =sqrt_alpha_M sqrt_alpha_m
33
34
# Gather \tilde (t-mm)
quant x gather output model, m,m, quant params)
37
Compute Atilde x (t-M) with stop gradient
38
quant_x_M = sg quant___M sg sg(quant_x_m) quant_x_m
Compute Loss for current step accuuuntt farch.mse(fp_xx. quant_x_M) g_m
41
42
43
# Update quantization parameters with accumulated gradients loss accuquant. sacuuuant.backward])
46
optimizer.stepl
47
48
# update indices
x fp_x_M
50
t-M
51
group index +=
21

---

A.2 Detailed derivations of Eq. (15)
We provide a detailed derivation of Eq. (15), We can represent the gradient between consecutive denoising steps for the quantized diffusion model as follows:
var- It + Voi
( (_va-ivi-a, V1- a--1
den (,, t)
(19)
Vai
Here, / the identity matrix, and (Gt 1) the output of the quantized model. We have empirically observed in Fig. 3 that the first term in Eq. (14) dominates the entire gradient, whereas the second
one is negligible. Based on this observation, we approximate the gradient Eq. (14) by omitting the second term as follows:
0ū.-1
10-11 I.
(20)
di,
Vai
Using Eq. (20) Eq. (16), we obtain the approximated gm follows:
m M
9m
M-m 0
m F M,
(21)
j=1
0è: M83
M
M-m dz, M 112
m * M,
(22)
Oos- M+3
m = M
(23)
jml
Vot-M++
M-1+1
m + M,
Var- M
I, for m = 1.,,..., M.
(24)
aa-m
A.3 Detailed derivation of the objective in Eq. (18) with the gradient approximation
We derive loss function in Eq. (18) incorporating our gradient approximation of Eq. (24). First, by substituting (24) into Eq. (12), we obtain:
aLSS
= 0LMSE
M
Io, m
9m
(25)
Os
di--M M
Ösi
Lm=1
I 2LMSE
/Oe-M s5t-m
(26)
0ir- M
/
Os:
M
Vas-M M 25
2(Tx-M M - S4- M)
(27)
Vat-m
Ist
Va--M 2( xc-M) m) M
(28)
Øs:
Note that we omit identity matrix in Eq. (24) for simple notation. From Eq. (28), we derive loss function whose gradient matches the derived expression by adding Ft-m and subtracting detached version of Zz-m within the squared term:
M
LAccoQuamt
Oit- M
[g( M - F1-M) + 8t-m - (g(8+mm) ml1
(29)
/a-m
m==1
In this formulation, we compute Iı-M and 7 before updating gradients without saving inter- mediate feature maps and treat as a constant during optimization. We then compute loss term inside the summation and accumulate its gradients progressively over multiple denoising steps. After completing M denoising steps, we update the step size using the cumulative gradient. The detailed pipeline of our method is provided in Algorithm 1.
22

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B Implementation details
For weight quantization, we adopt a uniform quantizer identical for all denoising steps, following
Q-Diffusion [25], since the weights remain invariant across different denoising steps. For the CIFAR-
10 [23], we employ the DDIM [49] with 100 total denoising steps, grouping them into 20 sets of 5 denoising steps each and setting learning rate in {1 x 10-S, 4 x 10 3. For the
[56],
we use LDM-4 [41] and the DDIM sampler [49] with 200 total denoising steps, grouping them into
20 sets of 10 denoising steps each and setting learning rate into 4 x 10 10-5, For the LSUN-Church [56],
use LDM-8 [41] and the DDIM sampler [49] with 500 total denoising steps, grouping them into 20 sets of 25 denoising steps each and setting learning rate into 4 x 10 5, For the ImageNet [6], employ LDM-4 [41] and the DDIM sampler [49] with 20 total denoising steps and forming 10 groups and setting learning rate into 1 x 10-3 For text-to-image generation, we employ Stable- Diffusion v1.4 3 with the PNDM sampler [31], using 50 total denoising steps and forming 25 groups and setting learning rate into 1 x 10 We set the calibration batch size to 8 for DDIM [49] and LDMs [41], and for Stable Diffusion J. All other experimental settings are identical those of Q-Diffusion [25]. We also retain the default settings [41] during the sampling phase, ensuring that we can conduct all experiments on a single A100 (80 GB) GPU. Also, to ensure a fair comparison, we quantize every layer of TFMQ-DM [19], such as attention-modules and skip-connections for unconditional image generation. Finally, we evaluate the FID [16] and IS [44] scores, including the FID2FP32 metric [50], using the torch- arch-fidelity library and the official Guided Diffusion [7] codebase.
C Detailed analysis of quantitative results
In this section, we analyze the quantitative results presented in Tables 1-3, Firstly, Table shows that AccuQuant outperforms other methods in most settings. In particular, AccuQuant achieves overwhelmingly superior performance on the FID2FP32 [50] metric across all bit-widths, and this effect becomes more pronounced at lower bit-widths ge.g.. 3/6 bits). Furthermore, AccuQuant achieves higher scores on the FID [16]. sFID [38], and IS [44] metrics compared to previous methods [25, 19, 54], which are not designed for reducing the accumulated quantization error. These findings indicate that AccuQuant effectively reduces accumulated quantization error allowing better performance and confirms that minimizing the accumulated quantization error constitutes a crucial factor in diffusion model quantization. Secondly, for the flass-coniiional image generation task reported in Table 2, we draw on previous work [54] showing that FID [16] does not perform reliably on ImageNet [6] and therefore we report LPIPS [59], PSNR, and SSIM metrics to quantify differences between the full precision and quantized models. Likewise to FID2FP32 [50], these metrics measure how closely the quantized model's outputs match those of the full precision model. We find that AccuQuant outperforms previous methods in terms of FID2FP32 [50]. LPIPS [59]. PSNR, and SSIM across all bit-widths, demonstrating that AccuQuant generates images that most closely resemble the full precision model's outputs while maintaining high visual quality. These results imply that accumulated quantization error remains critical even when employing few denoising steps, such as 20. Furthermore, even compared to PTOD [14], which is designed to reduce accumulating quantization error, AccuQuant outperforms it in FID2FP32 [50], LPIPS [59], PSNR, and SSIM across all bit widths, demonstrating the superiority of our framework in explicitly reducing accumulating quantization error. Finally, the text-to-image generation results in Table 3 reveal that, despite PCR [50] use of more bit-widths (i.e., 8.4 bits for activations) and adopting independent quantizer every denoising steps, AccuQuant achieves a better FID2FP32 [50] score. Additionally, AccuQuant attains the highest CLIP-Score [15], indicating that it not only reproduces images similar to the full precision model but also aligns them effectively with the text prompts. To this end, our findings demonstrate that the AccuQuant framework outperforms existing methods for reducing accumulated quantization error, and that AccuQuant not only achieves results comparable to those of the full-precision model but also confirms the fidelity term by resulting superior performance on FID [16], sFID [38], and CLIP score [15].
/tt http://inaaccccoooommmm/s//saaaa diffusion-onoooo v- o-iigiaaa htttt//://gttubb...o///ssss///// fidellt
Pnttps://hugginggacc
23

---

Figure 6: Visual comparisons of DDIM [49] for unconditional image generation on CIFAR-10 10 [23] under various group sizes. Both weights and activations were quantized to 6 bits for visually distinct and clear comparison. From top to bottom, the presented sequences correspond to the full full-precision model, method with group sizes of 1, 5, and 100.
Table 7: Quantitative comparisons of AccuQuant with and without the gradient approximation via various group sizes. We quantize DDIM [49] on CIFAR-I0 [23] under 4/8-bit setting.
FID / FID2FP32 +
Group size
w/o Approximation
w/ Approximation
6,88 / 3.11
6.88 3.11
5.26 2.32
4.75 1.15
10
5.27 1.62
5.07 1,88
5.73 1.49
5.24 1.49
Memory (MB)
40k
wlo Approximations
Approximations
30k
20k
10%
426
50
Group sizee
Figure 7: Comparisons of a total amount of memory of AccuQuant with and without the gradient approximation. We measure the memory usage during the calibration process of AccuQuant under 6/6-bit setting for DDIM [49] on CIFAR-10 [23].
D Qualitative results for group sizes
In this section, we present the qualitative results for various group sizes, as reported in Table 4. We observe from Fig. that selecting appropriate group size (e.g., group size of 5) generate images that closely resembling those of the full-precision model, under low bit-widhts. For example, in the first row of generated horse images, we can see that when the group size model fails to adequately account for accumulated errors, leading to the generation of distorted and unrealistic shapes. Similarly, when the group size is excessively large (c.g., group size of 100), the quantized model is unable to effectively manage the substantial accumulation of errors, resulting unrealistic image outputs. In contrast, with an appropriately chosen group size (e.g., group size of 5). the accumulated errors are effectively mitigated, allowing the generated images to maintain a structure and appearance comparable to those of full-precision model. the dog images of column 6, using group size of 5 yields images that most closely match the full-precision model in both texture and shape, outperforming group sizes I and 100. This indicates that an appropriate group sizes is crucial factor to mitigate the accumulating quantization error.
1, the quantized

---

1.4
Gradierz Magntuds
(bg34)
2.2-
1.00
0.8
0.04
0.030-
00005
280
180
160
140
120
100
80
20
450
409
200 Denoising Stop
250
150
100
Doncising Step
.SUNNBedrrom
L.SUN-Church
Figure 8: Plots of the gradient in Eq. (19) and its components denoising steps. The gradients calculated during a calibration process of AccuQuant for LSUN Bedroom [56] on the left and LSUN-Church [56] on the right.
Table 8: Quantization results for unconditional image generation with DPM-Solve+++ sampler [33] on CIFAR-10 (32 x 32) [23].
Model
Method
Bits(W/A)
IS1
FID./
FID2FP32J
Full-Precision
32/32
9.42
3.59
0.00
Q-Diffusion [25]
4/8
9.40
10.25
7.65
Ours
4/8
9.31
5.75
2.57
+ CIFAR-10
O-Diffusion [25]
4/6
7.88
52.65
49.21
(steps=50)
Ours
4/6
9.33
7.34
4,28
O-Diffusion [25]
3/8
9.57
40.41
39.04
Ours
3/8
9.11
22.36
20.90
E
Quantitative results for group sizes and gradient approximation
In this section, we show Table. 7 quantitative ablation results for varying group sizes, both with and without gradient approximation, for 4/t-bit quantized DDIM [49] CIFAR-10 [23]. We observe that both FID [16] and FID2FP32 [50] degrade at group sizes of and 25, since a group size of fails capture accumulated quantization error, whereas 25 is too large to find quantization parameters minimizing the error. This result highlights the importance of selecting appropriate group sizes and aligns with the findings discussed in the main paper. We also investigate the impact of gradient approximation. When the group size is 1, we calculate the gradient at every denoising steps and therefore the approximation has effect on performance. We show that using gradient approximation usually yields better performance, since the gradients of Eq. (14) are corrupted before the quantization parameters s, converge, leading unstable calibration process. We also show in Fig. total amount of memory of AccuQuant with and without the gradient approximation, w.r.t. the group size. The results show that the memory requirement grows linearly with group size the absence of the gradient approximation, whereas it remains constant across all group sizes when the approximation is applied. Consequently, omitting the noisy gradient term effectively reduce memory requirement and ensure calibration process stable.
F Gradient approximation across different dataset
In this section, visualize the gradient approximation LDM-4 and LDM-8 [41] across diverse datasets, including LSUN-Bedroom and LSUN-Church [56], as illustrated in Fig. 8. We plot the full gradients of Eq. (19), the gradient approximation of Eq. (20), and the residual term (i.e., C. d2 at 200 and 500 denoising steps. The results show that, consistent with the behavior observed in Fig. 8, the gradient approximation remains closely aligned with the full gradient throughout nultiple denoising steps both datasets, thereby corroborating the validity of our approximation. Moreover, as discussed in Table. and Table. 7, by omitting the residual term we avoid noisy updates during the calibration phase, resulting in more stable calibration process.
(a.
25

---

Figure 9: Visual comparisons of generated images on CIFAR-10 [23] (32x32) for unconditional image generation with 3rd order DPM-Solver++ [33] under 4/8-bit setting. From top to bottom, the presented sequences correspond to the Full precision, Q-Diffusion [25], and Ours.
G Evaluation with ad sampler
In this section, we report additional results for the advanced sampler (i.e., 3rd-order DPM- Solver++ [33]]. We have already reported performance for Stable Diffusion [41] with the PNDM sampler [31] in Table. 3. Here, we show in Table. a quantitative comparisons between our method and Q-Diffusion [25] for unconditional CIFAR-10 generation [23] over 50 denoising steps. For quantization, we devide the 50-step denoising process into 17 groups: the first 16 groups contain three consecutive steps each, and the final group contains two steps. We observe that our method consistently outperforms Q-Diffusion [25] in both FID [16] and FID2FP32 [50], demonstrating robustness across different samplers. Notably, in the 4/6-bit setting, our approach yields substantial gains, indicating enhanced tolerance to accumulated quantization error under low-bit activations. In Fig. 9, we present qualitative comparisons between our method and Q-Diffusion [25] under 4/8-bit quantization, It demonstrates that our approach recovers visual fidelity close to the full-precision model, whereas Q-Diffusion [25] produces visibly degraded outputs. This qualitative results further validates the ability of our method to mitigate accumulated quantization error.
H Additional visualization on various benchmarks
In this section, we show additional qualitative results for unconditional image generation, class- conditional image generation and text-to-image generation. For unconditional image generation, we conduct the LSUN-Bedroon [56] using LDM-4 [41] with 200 denoising steps, and LSUN- Church [56] using LDM-8 [41] with 500 denoising steps. The model weights and activations are quantized 3/8 bits respectively. As illustrated in Fig. 10 and Fig. 11, AccuQuant successfully prevents the accumulation of quantization errors, ensuring that generated images closely match their full precision counterparts with images containing rich semantics even in low-bit configurations. For example, in Fig. 10, we observe that Q-Diffusion [25] and TFMQ-DM [19] present an overall monotonous coloration compared the full precision results and generate different content of the bed due to the accumulated quantization error. contrast, AccuQuant preserves a coloration and the content similar to that of the full precision model. For class conditional image generation, we conduct the ImageNet [6] using LDM-4 [41] with 20 denoising steps and quantized weights and activations to 3/8 bits respectively. As illustrated in Fig. 12, Q-Diffusion [25] and TFMQ-DM [19], which do not account for accumulating quantization error, respectively exhibit chroma noise or produce monotone coloration. PTQD [14], which does account for accumulating quantization error, generates vivid colors but alters content compared to full precision and producing unrealistic artifacts such as chicken with two heads (i.e,, row 3, column in Fig. 12). In contrast, AccuQuant generates vibrant colors, realistic imagery, and outputs that closely match those of the full precision model. For text- to-image generation, we use COCO validation prompts [28] in Fig. 13 and user defined prompts in Fig. 14 with 50 denoising steps of Stable Diffusion v1.4 quantized into 4/8 bit-widths. As illustrated in Fig. 13, PCR [50], which is designed to mitigate accumulating quantization error, allocates more bit-width to activations yet still produces images with altered style distortion compared to the full precision model. In contrast, AccuQuant uses fewer quantizers and a lower bit-width than PCR [50] but effectively minimizes accumulated quantization error, generating realistic images that closely
26

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Table Computational cost of calibration process for DDIM [49] on CIFAR-I0 (32 32) [23] with 100 timesteps.
Method
Bits (W/A)
Batch size
Calibration time (h)
Energy (Wh)
FID
FID2FP32,
Full- PrelPreeciioon
32/32
4.26
0.00
Q-Diffusion [25]
6/6
5.97
519.39
30.46
35.24
Ours
6/6
5.56
561.56
5.79
3.30
Table 10: Computational cost of real-time CPU inference. Experiments are conducted on CIFAR-10
(32 32) [23] with DDIM [49] over 100 timesteps.
Method
Bits (W/A)
Batch size
GBops
Memory (MB)
CPU latency (s)
Model size (MB)
Speedup (x)
Full- Precision
32/32
6597
1726.0
94.589
143.08
1.00
O-Diffusion [25]
8/8
798
1541.7
31.322
36.57
3.02
Ours
8/8
64
798
1541.7
31.380
36.58
3.01
Table 11: Comparison against lightweight QAT. Experiments are conducted on ImageNet (256 x 256) [6] with LDM-4 [2] over timesteps. denotes result under the same resource constraint.
Method
W/A
Calibration time (h)
# of calibration data
FTD.
sFTD.
ISt
FID2FP32.
Pill-Precision
32/32
11.13
7.85
368.19
0.00
EfficientDM
4/8
4.34
5120 32 000
12.43
25.07
197.86
14.55
EflicientDM-Full (13)
4/8
6.50
9.92
7.40
351.79
1.63
Ours
4/8
4.34
$120
9.39
7.41
356.48
0.65
match those of the full precision model. We also visualize generated images conditioned on user defined prompts. As illustrated in Fig. 14, Q-Diffusion [25] and PCR [50] generates output that differ from those of the full precision model and misalign with the text prompt (e.g.. No astronaut in row 2, column 2 and row 3, column 4 in Fig. 14a), while AccuQuant align strongly with the prompts. In summary. AccuQuant not only achieves superior performance on quantitative evaluation metrics but also qualitatively generates images that most closely resemble full precision outputs among state-of-the methods, align strongly with the prompts, and exhibit naturalness and semantic richness, demonstrating the superiority of our framework.
I Computational cost and efficiency
In this section, provide detailed analysis of computational cost and efficiency in terms of calibration and inference. Tab. 9, we compare AccuQuant with Q-Diffusion [25] in terms of computational cost for calibration and the generation performance. We can that AccuQuant achieves superior performance with shorter calibration time compared to Q-Diffusion. We note that although AccuQuant may require more computational cost for one loss caleulation, it only requires 50 epochs per group. In contrast, Q-diffusion calibrates each layer and residual block for 5000 epochs. Although AccuQuant incurs a marginal increase in energy consumption, it delivers favorable trade-off for real-world deployment. In addition, we evaluate the inference efficiency of our quantized diffusion model against both Q-Diffusion and the full-precision baseline. Since the official PyTorch quantization API does not support bit-widths lower than 8, we quantize both weights and activations bits and measure the memory usage and runtime latency using ONNX Runtime with the Intel Xeon Gold 6226R CPU. As shown in Tab. 10, both quantized models achieve over a 3 times speedup compared to the FP model. Our method incurs marginally higher latency (by less than 0.18% and larger model size (by 0.006 MB) compared to Q-Diffusion, which we attribute to the separate quantization parameters per group. We also compare Tab. 11 AccuQuant with lightweight QAT approach, EfficientDM [13]. We report the results both under the same resource constraints
27

---

Table 12: Quantitative results for Gaussian deblurring on CelebA (256 256) [32].
Method
W/A
PSNR
LPIPS!
Full precision
32/32
31.23
0.0584
Q-Diffusion [25]
4/8
27.63
0.2131
Ours
4/8
30.57
0.0984
Q D-Diffusion [25]
3/8
24.70
0.4574
Ours
26.15
0.3979
Table 13:
Quantitative results for style transfer on the COCO validation set (512x512) [28]. We report SSIM, PSNR, LPIPS, style loss, content loss, and FID2FP32. All scores are calculated using the output of the full-precision model, since ground truth images are not available for style transfer.
Method
W/A
SSIM
PSNR
LPIPS|
Style loss
Content loss!
FID2EP321
O-Diffusion [25]
4/8
0.6645
18.50
0.3310
0.0012
13.2267 9.3687
14.20
Ours
4/8
0.7444
20.49
0.2594
0.0006
10.81
Table 14: Quantization results of DIT-XL/2 with 100 denoising steps on ImageNet (256 256) [23].
W/A denotes bit-widths of weights and activations. (a) without classifier- guidance. (b) with classifier-free guidance scale of 1.5.
Method
W/A
FID
SFID
Method
W/A
FID.
sFID
Full-precision
32/32
12.41
19.23
Full-precision
32/32
5.31
17.61
PTQ4DM [45]
4/8
213.66
85.11
PTQ4DM [45]
4/8
215.68
86.63
RepQ- VIT [27]
4/8
224.14
81.24
RepQ- ViT [27]
4/8
226.60
77.93
TFMQ-DM [19]
4/8
143.47
61.09
TEMQ-DM [19]
4/8
141.90
56.01
PTQ4DiT [52]
4/8
28.90
34.56
PTQ4DiT [52]
4/8
7.75
22.01
Ours
4/8
18.60
18.83
Ours
4/8
6.80
17.78
(a) without classifier-free guidance
(b) with classifier-free guidance
(denoted EfficientDM*) and using the official training recipe with larger training data and longer training time (denoted as EfficientDM-Full] We find that under an identical setting, AccuQuant achieves substantially better performance than EfficientDM* suggesting that QAT frameworks cannot converge sufficiently within limited resource budgets. Furthermore, although EfficientDM- Full benefits from extended training time and larger datasets, AccuQuant still outperforms it in terms of FID2FP32, demonstrating the effectiveness of our method. In summary, although our method marginally increases latency and model size compared to Q-Diffusion, the benefits of reduced calibration time and improved generation quality offer a favorable trade-off for practical deployment.
J Expanding to various tasks and advanced models
In this section, we demonstrate the generalization ability of AccuQuant by evaluating image restora- tion (e.g., Gaussian deblurring), style transfer, and applying transformer-basel diffusion mod- els [39]. For Gaussian deblurring, we leverage the pre-trained DDPG [10] model from the official GitHub repository
the CelebA dataset (256 256 resolution, 1K images) [32], injecting noise with Øy 0.05. Also, we use 100 total timesteps with group size of 5 and calibrate with 64 samples obtained from full-precision model. In Tab. 12, AccuQuant consistently outperforms
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Q-Diffusion [25] across both PSNR and LPIPS metrics, demonstrating its effectiveness in the restora- tion setting. For style transfer (Fig. 13), we use Stable Diffusion v1.4 with the prompt 'A cartoon style" and evaluated on the COCO validation set [28]. with the entire timestep of 35 using the DDIM sampler [49]. Since ground-truth images are unavailable for style transfer, we evaluate by comparing to the outputs obtained from the full-precision model. Note that we compute style and content losses following [11], using feature maps from a VGG network [47]. In Tab. 13, AccuQuant outper- forms all evaluated metrics, highlighting its robustness for diverse generative tasks beyond standard image synthesis. For transformer-based diffusion model [39] adaptation, we compare AccuQuant based quantization [52] and advanced transformer quantization method [27]. We conduct experiments on the ImageNet dataset [6] using the DiT-XL/2 [39] with 100 timesteps, under both without and with classifier-free free guidance settings [18]. As shown in Tab. 14, AccuQuant outperforms transformer- based, inffusiio-focused. and even Die--pecific quantization methods, demonstrating that reducing the accumulating error across diffusion timesteps is the key factor for quantizing diffusion models. In summary, by designing the quantization methods the diffusion framework level rather than for specific diffusion architecture, AccuQuant generalizes to diverse tasks and diffusion models.
to recent ieffusioonfocused quantization methods [45, 19] including
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Figure 10: Visual comparisons of generated images on [56] (256x256) for uncon- ditional image generation with LDMM- [41] under a 3/8-bit setting. Each row corresponds to Full Precision, Q-Diffusion [25]. TFMQ-DM [19], and Ours.
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shuft
Figure 11: Visual comparisons of generated images on LSUN-Church [56] (256x256) for uncon- ditional image generation with LDM-8 [41] under 3/8-bit setting. Each row corresponds to Full Precision, Q-Diffusion [25], TFMQ-DM [19], and Ours.
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Figure 12: Visual comparisons of generated images on ImageNet [6] (256x256) for class-conditional image generation with LDM-4 [41] under a 3/8-bit bit setting. Each row corresponds to Full Precision. Q-Diffusion [25], [14], TFMQ-DM [19], and Ours.
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"A colorful hot air balloon floating in blue sky above clouds."
"A table with some oranges and some cups."
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"Two elephants outdoors walking on green grass with trees nearby."
Figure 13: Visual comparisons of generated images (512x512) conditioned COCO validation prompts [28]. We generate images by SD v1.4 [41] and its quantized versions using Q-Diffusion [25] and AccuQuant under 4/8-bit setting and PCR [50] in 4/8.4 4/t.4-bit setting. Each row corresponds to Full Precision, Q-Diffusion [25], PCR(T 0.2) [50] and Ours.
34

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"An astronaut exploring alien planet with strange rock formations."
"A robot assistant helping modern kitchen." "
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"Cluttered house in the woods, anime, oil painting, high resolution, cottagecore, ghibli inspired"
Figure 14: Visual comparisons of generated images (512x512) conditioned on user defined prompts. We generate images by SD v1.4 [41] and its quantized versions using Q-Diffusion [25] and AccuQuant under 4/8-bit setting and PCR [50] in 4/8.4-bit setting. Each row corresponds Full Precision. O-Diffusion [25], PCR(T = 0.2) [50] and Ours.
36


Reviews:
[{"review_id": "DaBJZiYPn5", "reviewer": "Reviewer_YJ1y", "summary": "Prior work on post-training quantization (PTQ) has attempted to compress diffusion models by calibrating quantization parameters one step at a time, but ignores the fact that quantization errors accumulate across the sequence. This paper introduces AccuQuant, a novel PTQ method that explicitly addresses error accumulation. A key technical innovation is an efficient gradient approximation technique that reduces memory usage. Empirically, it achieves stronger fidelity to the full-precision model than prior quantization methods on a variety of benchmarks.", "questions": "1. Accumulation Quantization Error has been used in CNN architectures or Transformer architectures. Compared to literature works, how is current method different?\n\n2. The paper primarily compares with quantization methods specifically designed for diffusion models. However, it would strengthen the evaluation to include more recent diffusion-focused approaches such as PTQ4DM and Vidit-Q.\n\nAdditionally, since diffusion models often incorporate Transformer-based components, it would be valuable to compare against advanced Transformer quantization methods such as SmoothQuant and RepQ-ViT, to better assess general applicability and robustness\n\n[1] Repq-vit: Scale reparameterization for post-training quantization of vision transformers\n\n[2] Vidit-q: Efficient and accurate quantization of diffusion transformers for image and video generation.\n\n[3] Post-training quantization on diffusion models. \n\n[4] Smoothquant: Accurate and efficient post-training quantization for large language models. \n\n\n3. Understand the authors have conducted experiments on group size. However, will the optimal group size changes when dataset or model changes?\n\n4. The authors have conducted experiments analyzing the gradient approximation. Would it be possible to also compare the loss computed using full-precision models, rather than focusing solely on the quantized models?", "limitations": "Gradient approximation effects: The proposed gradient approximation makes the method feasible, but it is inherently an approximation. The paper does not deeply analyze whether this approximation affects the optimality of calibration. It is possible that the loss surface changes and the learned quantization parameters are suboptimal compared to a full-gradient approach (if that were practical). Quantifying any trade-off would strengthen the work. Not sure how the gradient approximation affect the overall loss.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. Novel multi-step calibration: Unlike previous PTQ approaches that minimize error per step in isolation, AccuQuant explicitly calibrates over groups of steps. This is a significant innovation: by “simulating” the sampling trajectory, the method directly accounts for the accumulated error from previous steps. This better aligns the quantized model’s outputs with the full-precision model over time, addressing a core limitation of existing methods.\n2. Memory-efficient implementation: The paper presents a clever gradient approximation that avoids storing all intermediate activations when backpropagating through multiple steps. This reduces memory complexity from $O(n)$ to $O(1)$, making multi-step calibration practical for large models. \n\nWeaknesses:\n1. Reproducibility (no released code): The authors state they do not release code due to copyright restrictions. Especially, some experimental results show their performance closer to benchmark.\n2. Variable gains at higher bit-widths: In some settings, the improvements over baselines are modest. For instance, on CIFAR-10 at 6/6 bits the gap between AccuQuant (FID=5.79) and the best prior (TFMQ-DM, FID=7.84) is clear, but at 4/8 bits the advantage is smaller (FID 4.75 vs TAC’s 4.89). This suggests that when models are already near full precision, the benefit may be incremental. It would be helpful to understand when multi-step calibration provides the biggest payoff (e.g. extremely low bits vs. moderate bits).", "was_revised": true, "final_justification": "Thanks for authors' reponse, it has addressed most of my concerns. However, the response to the questions of \"Variable gains at higher bit-widths\" is not convincing and aligned with the result in Table 1 to me. Even the performance may be related to the specific combination of precision of weights and activation. Therefore, I will still keep my score.", "rebuttal": "We sincerely appreciate the reviewer YJ1y for a thorough review and valuable comments. Below are our responses to the reviewer's concerns.\n\n---\n> W1. Reproducibility\n\nFor reproducibility, we have included a detailed description of the AccuQuant pipeline in Section 3. We have also provided an algorithm table and detailed hyperparameter settings for each experiment in the Appendix. Additionally, we present the following PyTorch-style pseudocode, which will be included in our paper upon acceptance.\n\n~~~\n# M : group size\n# x_T : random gaussian noise\n# fp_model : full-precision model\n# quant_model : quantized model\n# gather_output() : one iteration of diffusion denoising step\n# sg() : stop gradient operation\n\n# Initialize\nx_t = x_T\nt = T\ngroup_index = 0\n\nfor i in range(number_of_groups):\n    # Gather x_(t-M) from Full Precision Model\n    with torch.no_grad():\n        fp_x_M = gather_output(fp_model,x_t,t)\n\n    # Reconstruction stage\n        quant_model.set_group(group_index)\n    optimizer=torch.optim.Adam(quant_params,learning_rate)\n\n    for epoch in range(epochs):\n        # Gather \\tilde x_(t-M) with stop gradient\n        with torch.no_grad():\n            sg_quant_x_M = gather_output(quant_model,x_m,m,quant_params)\n        \n        optimizer.zero_grad()\n\n        # Accumulate the gradient\n        for m in range(M):\n            # Calculate gradient scaling factor\n            g_m =sqrt_alpha_M / sqrt_alpha_m\n\n            # Gather \\tilde x_(t-m)\n            quant_x_m = gather_output(quant_model,x_m,m,quant_params)\n\n            # Compute \\tilde x_(t-M) with stop gradient\n            quant_x_M = sg_quant_x_M - sg(quant_x_m) + quant_x_m\n\n            # Compute Loss for current step\n            loss_accuquant = torch.mse(fp_x_M - quant_x_M) * g_m\n\n            # Update quantization parameters with accumulated gradients\n            loss_accuquant.backward()\n        \n        optimizer.step()\n\n    # update indices\n    x_t = fp_x_M\n    t = t-M\n    group_index += 1\n    ...\n~~~\n\n---\n> W2. Variable gains at higher bit-widths \n\nAccuQuant mitigates accumulated quantization errors, which grow significantly in low-bit settings. We verify this in Table R1 by measuring the cosine distances between the outputs of full-precision and quantized model. By explicitly addressing the problem, AccuQuant delivers strong performance in such scenarios. While the problem is less severe in high-bit settings, AccuQuant still offers consistent improvements over prior methods, confirming its robustness. \n\n**Table R1**: Cosine distance between the outputs of the full-precision model and the quantized model across timesteps for various bit-width settings. Min-max quantization is applied to weights and activations.\n| Bitwidth | 100 | 80    | 60    | 40    | 20    | 0      |\n|----------|-----|-------|-------|-------|-------|--------|\n| 4/8      | 0   | 0.0084| 0.0269| 0.0796| 0.1698| 0.2032 |\n| 4/6      | 0   | 0.0782| 0.122 | 0.2098| 0.3799| 0.4523 |\n| 3/6      | 0   | 0.0819| 0.1624| 0.3298| 0.5842| 0.6864 |\n\n---\n> Q1. Accumulation Quantization Error has been used in CNN architectures or Transformer architectures. Compared to literature works, how is current method different?\n\nIn typical CNNs and transformers, quantization errors are accumulated only across the layers. However, in diffusion models, quantization errors are not only propagated through the layers but are also accumulated across different denoising steps. As a result, quantizing diffusion models requires a specialized approach that considers both the architectural and temporal aspects, which is more challenging and cannot be addressed sufficiently with conventional methods.\n\n---\n> Q2. Comparisons with recent diffusion-focused approaches and transformer quantization methods.\n\n**We compare in Table R2 AccuQuant to recent diffusion-focused quantization methods (PTQ4DM, PTQ4DiT) and advanced transformer quantization methods (RepQ-ViT).** We can see that AccuQuant achieves the best performance across all metrics, suggesting that AccuQuant is robust to architectures (e.g., CNNs, transformers).\n\nPlease note that our comparison with PTQ4DiT can be viewed as an indirect comparison with SmoothQuant as PTQ4DiT adopts a similar approach. Unfortunately, we were unable to include ViDiT-Q in our experiments. This method targets large-scale models (e.g., OpenSora), which require extensive computational resources, and adapting AccuQuant to these models was not feasible during the short rebuttal period.\n\n**Table R2** : Quantization results of DiT-XL on ImageNet (256×256). \n\n| Method        | W/A   | FID          | sFID    |\n|-----------------|-------|--------------|----------|\n| Full-precision           | 32/32 | 12.41        | 19.23    | \n| PTQ4DM         | 4/8   | 213.66       | 85.11    | \n| RepQ-ViT       | 4/8   | 224.14       | 81.24    |\n| TFMQ-DM        | 4/8   | 143.47       | 61.09    |\n| PTQ4DiT        | 4/8   | 28.90         | 34.56    |\n| Ours            | 4/8   | **18.60**         | **18.83**    | **5.60**      |\n\n---\n> Q3. Will the optimal group size changes when dataset or model changes?\n\nYes, the optimal group size can vary depending on the model architecture and dataset. We choose the group size to balance two factors: (1) capturing accumulated errors across the multiple timesteps, and (2) maintaining stable optimization. Using a small group size may fail to reflect errors accumulated over multiple timesteps, whereas using a large group size could complicate optimization due to the substantial accumulated error. We empirically found that splitting the whole timesteps into 10~20 chunks shows a good result in practice. As mentioned in the limitation section in the Appendix, we believe finding the optimal group size for different settings would be a promising direction for future research. \n\n---\n> Q4. Would it be possible to also compare the loss computed using full-precision models, rather than focusing solely on the quantized models?\n\nWe would like to clarify that computing gradients w.r.t the loss from a full-precision (FP) model is not feasible in our setup. This is because, as described in Eq. (11), we treat the FP model as a fixed ground truth reference while optimizing the quantized model. In this formulation, since the FP model is frozen during optimization, its loss gradients are not available for comparison.\n\nInstead of gradients w.r.t the loss, we compare in Table R3 the gradient between consecutive denoising steps (last term in Eq. (14)) between using the quantized diffusion model ($\\frac {\\partial \\tilde x_{t-1}} {\\partial \\tilde x_t}$) and the full-precision model ($\\frac{\\partial x_{t-1}}{\\partial x_t}$). We can see that the gradients of the quantized model have a much higher range than those of the full-precision model. As discussed in the paper, the Jacobian term ($ c_t \\frac{\\partial \\tilde\\epsilon_t}{\\partial \\tilde x_t}$) in the full gradient is noisy when the quantization parameters have not yet converged, and our gradient approximation removes this noise of the full gradient, resulting in a more stable and reliable optimization process for the quantized model.\n\n**Table R3** : Mean and min–max range of gradients computed every 20 timesteps. The first to third rows show results for the full-precision model, the quantized model, and our approximated gradient, respectively.\n\n| Timestep | 100 | 80 | 60 | 40 | 20 |\n|-----|-----|-----|-----|-----|-----|\n| $\\frac{\\partial\\tilde x_{t-1}}{\\partial\\tilde x_t}$ | 1.022 **(0.112)**| 1.059 **(0.059)**| 1.027 **(0.034)**| 1.008 **(0.034)**| 1.001 **(0.071)**|\n| $\\frac{\\partial x_{t-1}}{\\partial x_t}$ | 1.032 **(0.044)**| 1.060 **(0.050)**| 1.028 **(0.029)**| 1.008 **(0.023)**| 1.001 **(0.027)**|\n| $\\sqrt{\\frac{\\alpha_{t-1}}{\\alpha_{t}}}$ | 1.146 | 1.068 | 1.029 | 1.009 | 1.001 |\n\n\n---\n> L1. Loss landscape comparisons between full gradient and approximated gradient.\n\nWe’d like to clarify that both using the full gradient and our approximation share the same forward pass, meaning that the loss value is identical. Therefore, the loss surface itself does not change.\n\nAlthough the loss surface remains unchanged, the gradient approximation stabilizes optimization. We show in Table R4 the same statistics as in Figure 3 of the paper, but report the min-max range to better illustrate the variability of the gradients. The full gradients are highly variable and unstable, since unconverged quantization parameters result in a noisy Jacobian term ($\\frac{\\partial\\tilde\\epsilon_{t}}{\\partial\\tilde x_t}$), as discussed in Q4. In contrast, our gradient approximation omits the noisy Jacobian term and uses only the scalar coefficient, resulting in much more stable gradients. This leads to more stable convergence during calibration and ultimately yields more optimal results, as demonstrated in Table 5 in the paper.\n\n\n**Table R4**: Comparison of the full gradient and Jacobian term ($\\frac{\\partial\\tilde \\epsilon_{t}}{\\partial\\tilde x_t}$). The first row shows the full gradient between consecutive denoising steps from the quantized model, the second row shows the Jacobian term, and the third row shows our approximation. We report the mean and min-max range (max – min) of the gradient at every 20 timesteps.\n| Timestep | 100 | 80 | 60 | 40 | 20 |\n|-|-|-|-|-|-|\n| $\\frac{\\partial\\tilde x_{t-1}}{\\partial\\tilde x_t}$ | 1.0221  **(0.1119)** | 1.0586  **(0.0586)** | 1.0273  **(0.0343)** | 1.0082  **(0.0341)** | 1.0008  **(0.0711)** |\n| $\\frac{\\partial\\tilde \\epsilon_{t}}{\\partial\\tilde x_t}$ | -0.1236 **(0.1119)** | -0.0097 **(0.0586)** | -0.0015 **(0.0343)** | -0.0006 **(0.0341)** | -0.0002 **(0.0711)** |\n| $\\sqrt{\\frac{\\alpha_{t-1}}{\\alpha_{t}}}$ | 1.1457 | 1.0683 | 1.0288 | 1.0088 | 1.0010 |"}, {"review_id": "c2aIJ83SlL", "reviewer": "Reviewer_kHiT", "summary": "This paper proposes that PTQ for diffusion models should not be based solely on single-step denoising alignment, but rather on multi-step joint alignment to better account for accumulated errors. To address the high computational cost of aligning multiple steps, the authors introduce an efficient gradient approximation method based on empirical observations. Extensive experiments demonstrate that the proposed approach achieves state-of-the-art PTQ performance for diffusion models.", "questions": "1. Could enforcing multi-step alignment lead to suboptimal results? For example, if we keep the same calibration process but only include the loss between the final-step outputs of the quantized and full-precision models, could that potentially lead to better optimization? This concern may be reflected in Table 4, where increasing the group size actually leads to performance degradation.\n2. What is the actual computational overhead of the proposed multi-step joint optimization? Given the complexity, would a lightweight QAT approach achieve better results with similar resource costs?\n3. Why does removing gradient approximation lead to worse results? The results in Table 5 are counterintuitive. This may suggest that the optimization objective in Equation (12) is inherently flawed, as also questioned in Point 1 above.", "limitations": "No further discussion is needed.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### Strengths\n\n1. The paper presents a clear and well-motivated rationale for aligning multiple denoising steps to mitigate cumulative errors, and accordingly introduces a novel and reasonable optimization objective.\n2. The authors thoroughly consider the computational complexity involved in aligning cumulative errors and effectively address it through mathematical reformulation and gradient approximation techniques.\n3. Extensive experiments demonstrate that the proposed method consistently outperforms existing PTQ approaches for diffusion models across multiple evaluation dimensions.\n\n### Weaknesses\n\n1. Increasing the group size consistently leads to suboptimal results, which is rather puzzling. This may suggest that the alignment objectives defined in Equations (10) and (12) are potentially inaccurate or not well-justified.\n2. The manuscript does not report the overall cost of the proposed method, including actual runtime and memory efficiency, which are crucial for evaluating its practical applicability.", "was_revised": true, "final_justification": "Although the choice of group size is based on practical considerations rather than perfect theoretical backing, I still acknowledge the innovative contributions presented in the manuscript.", "rebuttal": "We sincerely appreciate the reviewer kHiT for a thorough review and valuable comments. Below are our responses to the reviewer's concerns.\n\n> W1, Q1: Increasing the group size consistently leads to suboptimal results, which is rather puzzling. This may suggest that the alignment objectives defined in Equations (10) and (12) are potentially inaccurate or not well-justified.\n\nIt may seem ideal to set the group size equal to the total number of timesteps, as it minimizes the final accumulated error directly; however, this approach often leads to suboptimal quantization parameters in practice. When the group size is excessively large, the accumulated error becomes substantial. This makes it difficult to optimize the quantization parameters effectively, resulting in suboptimal performance. Therefore, the group size should balance the trade-off between capturing long-range accumulated error and maintaining stable optimization. We believe finding the optimal group size for different settings would be a promising direction for future research, as mentioned in the limitations in the Appendix.\n\n---\n> W2: The manuscript does not report the overall cost of the proposed method, including actual runtime and memory efficiency, which are crucial for evaluating its practical applicability.\n\nIn Table R5, we compare AccuQuant with Q-Diffusion in terms of computational performance and generation quality. We can see that AccuQuant achieves superior performance with shorter calibration time compared to Q-Diffusion. We note that although AccuQuant may require more computational cost for one loss calculation, it only requires 50 epochs per group. In contrast, Q-diffusion calibrates each layer and residual block for 5000 epochs. Although AccuQuant incurs a marginal increase in energy consumption, it delivers a favorable trade-off for real-world deployment.\n\nIn addition, we evaluate the inference efficiency of our quantized diffusion model against both Q-Diffusion and the full-precision (FP) baseline. Since the official PyTorch quantization API does not support bit-widths lower than 8, we quantize both weights and activations to 8 bits and measure the memory usage and runtime latency using ONNX Runtime with the Intel Xeon Gold 6226R CPU. As shown in Table R6, both quantized models achieve over a 3 times speedup compared to the FP model. Our method incurs a marginally higher latency (by less than 0.18%) and larger model size (by 0.006 MB) compared to Q-Diffusion, which we attribute to the separate quantization parameters per group.\n\nIn summary, although our method marginally increases latency and model size compared to Q-Diffusion, the benefits of reduced calibration time and improved generation quality offer a favorable trade-off for practical deployment.\n\n\n**Table R5**: Calibration computational overhead for DDIM CIFAR-10 with 100 timesteps.\n| Method   | Bits (W/A) | Batch size | Calibration time (hours) | Energy (Wh) | FID↓ | FID2FP32↓ |\n|---------------|------------|------------|--------------------------|-------------|-------|----------|\n| **FP**      | 32/32  | 8    | –           | –     | 4.26 | 0   |\n| **Q-Diffusion** | 6/6   | 8    | 5.97          | **519.39**  | 30.46 | 35.24 |\n| **Ours**     | 6/6   | 8    | **5.56**          | 561.56  | **5.79** | **3.3**  |\n\n\n**Table R6** : Computational cost of real-time CPU inference. Experiments are conducted in CIFAR-10 with DDIM over 100 timesteps\n| Method    | Bits (W/A) | Batch size | GBops | Memory(MB)  | CPU latency(s) | Model size(MB) | x Speed up |\n|--------------------|------------|------------|--------------------|------------|-------------|------------|------------|\n| **FP**    | 32/32  | 64   | 6597    | 1726  | 94.589  | 143.08 | x1   |\n| **Q-Diffusion** | 88   | 64   | 798    | 1541.7 | 31.322  | 36.57 | x3.02  |\n| **Ours**   | 88   | 64   | 798    | 1541.7 | 31.38  | 36.58 | x3.01  |\n\n\n---\n> Q2: What is the actual computational overhead of the proposed multi-step joint optimization? Given the complexity, would a lightweight QAT approach achieve better results with similar resource costs?\n\nWe compare in Table R7 AccuQuant with a lightweight QAT approach, EfficientDM [1]. We report the results both under the same resource constraints (denoted as EfficientDM*) and using the official training recipe with larger training data and longer training time (denoted as EfficientDM-Full). We find that under an identical setting, AccuQuant achieves substantially better performance than EfficientDM*, suggesting that QAT frameworks cannot converge sufficiently within limited resource budgets. Furthermore, although EfficientDM-Full benefits from extended training time and larger datasets, AccuQuant still outperforms it in terms of FID2FP32, demonstrating the effectiveness of our method once again.\n\n**Table R7**: Comparison against lightweight QAT. Experiments are conducted in ImageNet 256×256 with LDM-4 over 20 timesteps\n| Method        | W/A | Training time (hours) | # of training data | FID↓ | sFID↓ | IS↑   | FID2FP32↓ |\n|----------------------|------|-----------------------|--------------------|-------|-------|---------|-----------|\n| **EfficientDM\\***    | 4/8 | 4.34         | 5120        | 12.43 | 25.07 | 197.86 | 14.55   |\n| **EfficientDM-Full** | 4/8 | 6.5          | 32000       | 9.92   | **7.40**   | 351.79    | 1.63     |\n| **Ours**       | 4/8 | 4.34         | 5120        | **9.39** | 7.41 | **356.48** | **0.65**   |\n\n[1] : EfficientDM: Efficient Quantization-Aware Fine-Tuning of Low-Bit Diffusion Models, ICLR, 2024\n\n---\n> Q3: Why does removing gradient approximation lead to worse results? This may suggest that the optimization objective in Equation (12) is inherently flawed\n\nAlthough the full gradient without approximation (Eq. (14)) is expected to provide the most accurate optimization direction, our empirical results demonstrate that it leads to unstable and difficult convergence. The key reason is that the quantization parameters have not yet converged, which results in large output changes in response to small input variations and consequently leads to a noisy Jacobian term ($\\frac{\\partial\\tilde \\epsilon_{t}}{\\partial\\tilde x_t}$).\nIn Table R4 (refer to the answer L1 in YJ1y), the Jacobian component is smaller in average magnitude compared to the dominant scalar component, but it exhibits a high dynamic range, which introduces substantial noise into the full gradient (up to 21% at peak, and above 6% for most timesteps). Therefore, we approximate the full gradient by omitting the Jacobian term and utilizing only the dominant scalar component. This removes undesirable noise effectively while preserving the overall mean gradient magnitude and the relative proportions of gradients across timesteps.\nAs a result, our method enables a more stable and reliable optimization process. In summary, the results in Table 5 do not indicate a fundamental flaw in the optimization objective itself, but rather show that, in practice, the real gradient is dominated by high-frequency noise due to the Jacobian term."}, {"review_id": "6vAT7yylb8", "reviewer": "Reviewer_iFPY", "summary": "This paper proposes AccuQuant, a novel post-training quantization method for diffusion models that reduces accumulated quantization errors by simulating multiple denoising steps during quantization. It also introduces a memory-efficient objective and demonstrates strong performance across various tasks and models.", "questions": "1:How does AccuQuant determine the optimal number of denoising steps to simulate during quantization to balance accuracy and efficiency?\n\n2: How good does AccuQuant generalize to tasks beyond image generation, such as image restoration ( a small scale experiment  will do)?\n\n3: What are the trade-offs regarding computational cost between AccuQuant and previous step-wise quantization methods during the quantization process?", "limitations": "The major limitation of this work is its adaptation to other domains such as inpainting, restoration etc.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strength: The paper presents a strong motivation by identifying and analyzing the unique challenge of error accumulation in quantized diffusion models. The presented AccuQuant is a thoughtful approach by simulating multiple denoising steps during quantization, aligning closely with the actual inference behavior of diffusion models. This is a meaningful departure from prior per-step quantization strategies. The thorough evaluation on standard benchmarks strengthens showcases real-world applicability.\nWeakness:\n1: In the paper, the method is tested across various diffusion models and benchmarks, it’s unclear if tasks beyond generation (e.g., image restoration, inpainting, or editing) were considered, if these tasks can’t be evaluated, it is better to give reasonable explanations.\n2: The work has a strong assumption that minimizing output discrepancies over a few denoising steps is sufficient to mitigate long-range error accumulation. But some error behaviors might emerge only over longer sampling chains, the authors should explain this issue more. \n3. Although the paper introduces an efficient implementation (O(1) memory), there may still be computational overhead in simulating multiple denoising steps during quantization, especially for large-scale models. A more detailed analysis of runtime and energy trade-offs during quantization would help others understand its deployment feasibility.", "was_revised": true, "final_justification": "I thank the authors for their efforts in addressing all my concerns. As all my questions have been satisfactorily answered, I will raise my score accordingly.", "rebuttal": "We sincerely appreciate the reviewer iFPY for a thorough review and valuable comments. Below are our responses to the reviewer's concerns.\n\n> W1, Q2, L1. it’s unclear if tasks beyond generation (e.g., image restoration, inpainting, or editing) were considered, if these tasks can’t be evaluated, it is better to give reasonable explanations.\n\nThank you for this valuable suggestion. The experiments reported in the main paper were conducted using the standard benchmarks for diffusion model quantization. However, following your comment, we present experimental results on tasks beyond image generation, including image restoration (Gaussian deblurring) and style transfer.\n\nFor image restoration, we leverage the pre-trained DDPG [1] model from the official GitHub repository on the CelebA dataset (256 × 256 resolution, 1K images), injecting noise with σᵧ = 0.05. Also, we use 100 total timesteps with a group size of 5 and calibrate with 64 samples obtained from a full-precision model. In Table R8, AccuQuant consistently outperforms Q-Diffusion across both PSNR and LPIPS metrics, demonstrating its effectiveness in the restoration setting.\n\nFor style transfer, we use Stable Diffusion v1.4 with the prompt ‘A cartoon style’, evaluated on the COCO validation set, with the entire timestep of 35 using the DDIM sampler. In Table R9, AccuQuant outperforms all evaluated metrics, highlighting its robustness for diverse generative tasks beyond standard image synthesis.\n\n\n**Table R8** : Quantitative results for Gaussian deblurring on CelebA 256×256. We report PSNR and LPIPS for w4a8 and w3a8 settings, comparing our method with Q-Diffusion.\n| Method            | W/A   | PSNR   | LPIPS (w.r.t GT) |\n|------------------------------|-------|--------|------------------|\n| Full precision               | 32/32 | 31.23  | 0.0584           |\n| Q-Diffusion                  | 4/8   | 27.63  | 0.2131           |\n| **Ours**                     | 4/8   | **30.57** | **0.0984**     |\n| Q-Diffusion                  | 3/8   | 24.7   | 0.4574           |\n| **Ours**                     | 3/8   | **26.15** | **0.3979**     |\n\n\n**Table R9**: Quantitative results for style transfer on the COCO validation set (512×512). We report SSIM, PSNR, LPIPS, style loss, content loss, and FID2FP32. All scores are calculated using the output of the full-precision model, since ground truth images are not available for style transfer.\n|Method  | W/A | SSIM | PSNR | LPIPS | Style loss | Content loss | FID2FP32 (5k) |\n|-------------|-----|--------------|--------------|---------------|--------------------|----------------------|---------------|\n| Q-Diffusion | 4/8 | 0.6645       | 18.5         | 0.331         | 0.0012             | 13.2267              | 14.2          |\n| **Ours**    | 4/8 | **0.7444**   | **20.49**    | **0.2594**    | **0.0006**         | **9.3687**           | **10.81**     |\n\n[1] Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance, CVPR, 2024\n\n---\n> W2. Is it sufficient to minimizing output discrepancies over a few denoising steps?\n\nIt may seem intuitive to use a very large group size to directly account for long-range error accumulation. However, our experiments show that dividing the timesteps into smaller groups is an effective way to substantially reduce accumulated error in diffusion model quantization. By optimizing quantization parameters for each group, we can address error accumulation locally. This approach yields much lower total accumulated error compared to considering long-range error accumulation with excessively large group sizes, as shown in Table 4. This is because, when the group size is excessively large, the accumulated error becomes substantial. This makes it difficult to optimize the quantization parameters effectively, resulting in suboptimal performance. Therefore, the group size should balance the trade-off between capturing long-range accumulated error and maintaining stable optimization. \n\n\n---\n> Q1. How to determine the optimal number of group size?\n\nThe group size is treated as a hyperparameter that balances two objectives: (1) sufficiently capturing accumulated errors across multiple timesteps, and (2) ensuring stable optimization of quantization parameters. As shown in the results, if the group size is too small, it may fail to capture the long term error accumulation; if it is too large, the optimization becomes unstable as a single set of parameters must account for the diverse behaviors of many timesteps. The optimal group size can vary depending on the model and dataset, but we empirically found that dividing the timesteps into 10 to 20 groups yields consistently strong results across our experiments.\nAs mentioned in the limitation section in Appendix, we believe finding the optimal group size for different settings would be a promising direction for future research.\n\n\n---\n> W3, Q3. A more detailed analysis of runtime and energy trade-offs compared to previous step-wise quantization methods during quantization.\n\nIn Table R10, we compare AccuQuant with Q-Diffusion in terms of computational overhead, specifically calibration time (GPU hours on A6000 GPU) and average energy consumption during calibration (Wh). We can see that AccuQuant achieves both faster calibration time and superior performance compared to Q-Diffusion. Although AccuQuant may require more computational cost for one loss calculation, we find that 50 epochs per group are sufficient for the quantization parameters to converge. In contrast, Q-diffusion calibrates each layer and residual block for 5000 epochs. Although AccuQuant incurs a marginal increase in energy during calibration due to the multi-step optimization, AccuQuant achieves substantially enhanced performance with shorter calibration time, making it a favorable trade-off for real-world deployment\n\n\n**Table R10**: Calibration computational overhead for DDIM CIFAR-10 with 100 timesteps.\n| Method   | Bits (W/A) | Batch size | Calibration time (hours) | Energy (Wh) | FID↓ | FID2FP32↓ |\n|---------------|------------|------------|--------------------------|-------------|-------|----------|\n| **FP**      | 32/32  | 8    | –           | –     | 4.26 | 0   |\n| **Q-Diffusion** | 6/6   | 8    | 5.97          | **519.39**  | 30.46 | 35.24 |\n| **Ours**     | 6/6   | 8    | **5.56**          | 561.56  | **5.79** | **3.3**  |"}, {"review_id": "L5DDse3617", "reviewer": "Reviewer_W9wt", "summary": "The paper proposes a method to quantize diffusion models for image generation post training that is more robust than state-of-the-art techniques, providing better image quality at the same quantization bit width. The main idea is to optimize the quantization process by jointly considering multiple timesteps of the diffusion process in order to prevent accumulation of quantization errors. This is also implemented efficiently via a gradient approximation approach that avoids backpropagation though the selected group of timesteps in sampling chain.", "questions": "The fact that the approximated gradients work better than the \"correct\" counterpart is quite surprising. The authors attempt an explanation suggesting that that the removed term is quite noisy but I am not fully convinced by this explanation. The method without approximation should minimize Eq. (11) having the full precision result as ground truth and the current denoiser, so how is it possible that the correct objective is noisier than the simplified objective? Is it possible this might be due to small batch size for the experiment without approximation?", "limitations": "Some limitations are acknowledged in the Appendix. The authors should integrate them in the main text. Societal impact of more efficient generative models is not discussed.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- the paper is overall well written and clearly motivated\n- the method seems novel and it is is scientifically sound. The idea to jointly consider multiple timesteps when optimizing the quantization process indeed allows to attenuate the error accumulation process of models optimizing individual timesteps\n- experimental results are extensive enough to properly characterize the performance of the method compared to the state-of-the-art under various quantization bit widths and to assess the design decisions such as the gradient approximation\n\nWeaknesses:\n- some minor presentation issues. For example: the FID2FP32 metric is mentioned in the introduction before being defined and may confuse readers. Also, it needs some explanation why we need this metric and it is not enough to just measure the regular FID\n- results are good but they are not always the best. It seems that for the experiments where numbers are reported, TAC [43] is a strong baseline. The authors should better discuss this method.\n- The ablation on the group size suggest that beyond a certain size the proposed method will result in (significantly) worse performance than working independently on each timestep. It is not very clear how one would choose the optimal group size.\n- It would be interesting to check the performance of the method on recent models using very few timesteps, so that a single group could be formed for optimization", "was_revised": true, "final_justification": "The method is sufficiently novel, theoretically justified and has good experimental performance. Authors addressed some of the minor points I raised in a satisfactory manner.", "rebuttal": "We sincerely appreciate the reviewer W9wt for a thorough review and valuable comments. Below are our responses to the reviewer's concerns.\n\n> W1. Some minor presentation issues. For example: the FID2FP32 metric is mentioned in the introduction before being defined and may confuse readers. Also, it needs some explanation why we need this metric and it is not enough to just measure the regular FID. \n\nFID2FP32 measures the FID score between the outputs of the quantized and full-precision models. In diffusion model quantization, the standard FID alone is insufficient because it only evaluates the generative quality with respect to real images, not how well the quantized model replicates the behavior of its original full-precision counterpart. Therefore, FID2FP32 is necessary to specifically quantify the performance drop caused by quantization by directly measuring the similarity between quantized and full-precision model outputs. We will add a clear definition of FID2FP32 and an explanation of why it is needed.\n\n\n---\n> W2. Results are good but they are not always the best. It seems that for the experiments where numbers are reported, TAC is a strong baseline. The authors should better discuss this method.\n\nTAC assumes that the output of the quantized model can be represented as a simple linear combination of the full-precision output and two coefficients (i.e., $\\tilde\\epsilon = a\\epsilon + b$), and compensates for the quantization error using these coefficients obtained during calibration. However, in low-bit quantization settings, we observe that this formulation is not valid due to the large accumulated errors. We report in Table R11 the $R^2$ (coefficient of determination from linear regression) scores between the output of a full-precision model and the quantized models for both $\\epsilon_t$ and $x_t$. Notably, the $R^2$ value is lower for the 3/6 and 4/6-bit setting than for the 4/8-bit setting, indicating that the full-precision outputs are not accurately regressed with the quantized outputs under low-bit settings. This explains the suboptimal performance of TAC in low-bit settings, as observed in Table 1 (e.g., 3/6 bits for DDIM CIFAR-10 and 3/8 bits for LDM Churches). Additionally, TAC requires extra computation to compensate for the error during the inference phase, which can further limit its efficiency.\n\nIn contrast, AccuQuant minimizes the accumulated quantization error directly by optimizing the quantization parameters through a gradient-based approach. This allows AccuQuant to more effectively capture the non-linear relationship between quantized and full-precision outputs, resulting in superior performance, especially in challenging low bit-width regimes. This is why AccuQuant achieves superior performance compared to TAC in low-bit settings. Furthermore, our method does not require any additional operations during the inference phase.\n\n\n**Table R11**: $R^2$ scores between the outputs of the quantized and full-precision models for $\\mathbf{x}_t$ and $\\boldsymbol{\\epsilon}_t$. The $R^2$ scores are computed using the scikit-learn package.\n\n| bit-width  | 4/8   | 4/6   | 3/6   |\n|--------|------|------|------|\n| $x_t \\to \\tilde x_t$   | 0.91 | 0.68 | 0.39 |\n| $\\epsilon_t \\to \\tilde \\epsilon_t$ | 0.92 | 0.71 | 0.62 |\n\n\n---\n> W3. The ablation on the group size suggest that beyond a certain size the proposed method will result in (significantly) worse performance than working independently on each timestep. It is not very clear how one would choose the optimal group size.\n\nIt may seem ideal to set the group size equal to the total number of timesteps, as it minimizes the final accumulated error directly; however, this approach often leads to suboptimal quantization parameters in practice. When the group size is excessively large, the accumulated error becomes substantial. This makes it difficult to optimize the quantization parameters effectively, resulting in suboptimal performance. \n\nTherefore, the group size should balance the trade-off between capturing long-range accumulated error and maintaining stable optimization. In our settings, we treat group size as a hyperparameter, chosen to balance two factors: (1) capturing accumulated errors across the multiple timesteps, and (2) maintaining stable optimization of quantization parameters. We empirically found that splitting the whole timesteps into 10~20 chunks shows a good result in practice. We believe finding the optimal group size for different settings would be a promising direction for future research, as mentioned in the limitations in the Appendix.\n\n\n---\n> W4. It would be interesting to check the performance of the method on recent models using very few timesteps, so that a single group could be formed for optimization\n\nThank you for this excellent suggestion. In response, we present in Table R12 our quantization results on a distilled diffusion model with very few timesteps. Specifically, we use PD [1] with a total of 8 steps (W4A8 bits, CelebA 256×256), applying quantization to the pre-trained distilled model provided from the official GitHub. We summarize our findings as follows: \n(1) AccuQuant consistently outperforms Q-Diffusion across all metrics. This indicates that AccuQuant generalizes well even to distilled models with very few denoising steps. \n(2) Group size 1 yields lower performance compared to group sizes 4 and 8. This suggests that mitigating accumulated error remains important, even for models distilled to only a few timesteps.\n(3) Group size 4 is superior to group size 8 for certain metrics. This implies that, even when the total number of timesteps is small, setting the group size to include all steps (i.e., a single group) is not always optimal. This finding reinforces our earlier discussion regarding the trade-offs of group size selection.\n\n**Table R12**: Quantitative results for PD [1] on CelebA 256x256. We report FID2FP32, LPIPS, PSNR, and SSIM\n|  Method     | FID2FP32 | LPIPS  | PSNR    | SSIM   |\n|----------------|----------|--------|---------|--------|\n| QDiff          | 33.31    | 0.2696 | 22.3109 | 0.8312 |\n| Ours (group size 1)   | 23.154   | 0.2051 | 24.1612 | 0.9193 |\n| Ours (group size 4)   | **13.49**    | 0.1768 | **25.3458** | 0.9282 |\n| Ours (group size 8)   | 14.219   | **0.1648** | 24.7452 | **0.9299** |\n\n\nreferences:\n[1] Progressive Distillation for Fast Sampling of Diffusion Models, ICLR, 2022\n\n---\n> Q1. how is it possible that the correct objective is noisier than the simplified objective? Is it possible this might be due to small batch size for the experiment without approximation?\n\nAlthough the full gradient without approximation (Eq. (11)) is theoretically expected to provide the most accurate optimization direction, our empirical results demonstrate that this is not always true in practice. The key reason lies in the Jacobian term, which is present in the full gradient but omitted in our approximation.\n\nAs discussed in answer L1 of YJ1y, the Jacobian component is significantly smaller in average magnitude compared to the dominant scalar component, but it exhibits a high dynamic range—introducing substantial noise into the full gradient. This high-variance noise causes the quantization parameters to change inconsistently at each step, leading to an unstable and unreliable calibration process. In contrast, our approximation excludes the noisy Jacobian term and utilizes only the dominant scalar component, effectively removing this undesirable noise while preserving the overall mean gradient magnitude and the relative proportions of gradients across timesteps. As a result, our method enables a more stable and reliable optimization process."}]

Author rebuttal:

Meta-review: This paper proposes AccuQuant, a novel post-training quantization method for diffusion models that reduces accumulated quantization errors by simulating multiple denoising steps during quantization. The proposed method is well-motivated, scientifically sound, and demonstrates consistent improvements over prior PTQ approaches across multiple benchmarks. Before the rebuttal, the reviewers raised concerns, including limited code availability, modest gains at higher bit-widths, and some open questions regarding computational overhead, group size selection, and generalization to other tasks. The authors have addressed these concerns during the rebuttal; therefore, I would like to recommend accepting this paper.
Decision: Accept (poster)