Diffusion Models Beat GANs on Image Synthesis
Authors: Prafulla Dhariwal
Alexander Quinn Nichol
Venue: NeurIPS 2021 Spotlight (2021)
Keywords: generative models
diffusion models
score-based models
denoising diffusion probabilistic models
image generation
neural networks
attention

Abstract: We show that diffusion models can achieve image sample quality superior to the current state-of-the-art generative models. We achieve this on unconditional image synthesis by finding a better architecture through a series of ablations. For conditional image synthesis, we further improve sample quality with classifier guidance: a simple, compute-efficient method for trading off diversity for fidelity using gradients from a classifier. We achieve an FID of 2.97 on ImageNet 128$\times$128, 4.59 on ImageNet 256$\times$256, and 7.72 on ImageNet 512$\times$512, and we match BigGAN-deep even with as few as 25 forward passes per sample, all while maintaining better coverage of the distribution. Finally, we find that classifier guidance combines well with upsampling diffusion models, further improving FID to 3.94 on ImageNet 256$\times$256 and 3.85 on ImageNet 512$\times$512.

Diffusion Models Beat GANs on Image Synthesis
Prafulla Dhariwal"
Alex Nichol" OpenAl al alex@openai.com com
OpenAl prafulla@openai.com com
Abstract
We show that diffusion models achieve image sample quality superior to the current state-of ttate-of-the-art generative models. We achieve this on unconditional image synthesis by finding better architecture through series of ablations. For condi- tional image synthesis. we further improve sample quality with classifier guidance: simple, compute-cfficee -fficceett method for trading off diversity for fidelity using gradi- ents from a classifier. We achieve an FID of 2.97 on ImageNet 128 128, 4.59 on ImageNet 256x256 and 7.72 ImageNet 512x512, and match BigGAN-deep even with as few as 25 forward passes per sample, all while maintaining hetter coverage the distribution. Finally, find that classifier guidance combines well with upsampling diffusion models, further improving FID to 3.94 on ImageNet 256 256 and 3.85 ImageNet 512x512.
Introduction
Figure Selected samples from our best ImageNet 512x512 model (FID 3.85)
Over the past few years, generative models have gained the ability generate human-like natural language [ high-quality synthetic images [8] 34 57 and highly diverse human speech and music
These models can be used in variety of ways, such generating images from text prompts or learning useful feature representations [88 10 While these models are already capable
56
"Equal contribution
35th Conference on Neural Information Processing Systems (NcurIPS 2021).

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of producing realistic images and sound, there is still much room for improvement beyond the current state-of-the-are and better generative models could have wide-ranging impacts on graphic design. games, music production, and countless other fields.
GANs 2 currently hold the oate--of-the-are on most image generation tasks
+4
as measured
by sample quality metrics such as FID [29]. Inception Score [6]] and Precision
38 However, some
of these metries do not fully capture diversity, and has been shown that GANs capture less diversity than state-of-the-art train, collapsing without carefully selected hyperparameters and regularizers
sreeihoodd-assee models [57 4o 4
Furthermore, GANs are often difficult to
N 4 77. While GANs
their drawbacks make them difficult to scale and apply to new domains. As result, much work has been done to achieve GAN-like sample quality with likelihood-biae based models [22] [57 31 48 [12. While these models capture more diversity and are typically easier to scale and train than GANs, they still fall short in terms of visual fidelity. Furthermore, except for VAEs, sampling from these models is slower than GANs in terms of wall-clock time.
hold the saate-of-hhe-se
Diffusion models are a class of likelihood-basee models which have recently been shown to produce high-quality images [63 66 31 40
while offering desirable properties such as distribution coverage, stationary training objective, and easy scalability. These models generate samples by gradually removing noise from a signal, and their training objective can be expressed as a reweighted variational lower-bound [3I. This class of models already holds the state-of- th-tth- [7 on CIFAR-10 37, but still lags behind GANs on difficult generation datasets like LSUN and ImageNet. We hypothesize that this gap exists for at least two reasons: first, that the model architectures used by recent GAN literature have been heavily explored and refined; second, that GANs are able to trade off diversity for fidelity, producing high quality samples but not covering the whole distribution. We aim to bring these benefits to diffusion models, first by improving model architecture and then by devising a scheme for trading off diversity for fidelity.
The rest of the paper is organized as follows. In Section 2. we give a brief background of diffusion models based on Ho et al. 3 and the improvements from Nichol and Dhariwal 4 and Song
et al. 164,, and we describe our evaluation setup. In Section 3 we introduce simple architecture
improvements that give a substantial boost to FID. In Section 4 we describe a method for using
we show that models with our improved architecture achieve state-of-the-an on unconditional image synthesis
gradients from classifier to guide a diffusion model during sampling. Finally, in Section 5
tasks, and with classifier guidance achieve state-of-the-arr on conditional image synthesis.
Background
In this section, we provide a brief overview of diffusion models. For a more detailed mathematical description, we refer the reader to Appendix C On high level, diffusion models sample from distribution by reversing a gradual noising process. In particular, sampling starts with noise Fr and produces gradually less-noisy samples 27-1. 2T-2,- ... until reaching final sample To- In particular, a diffusion model learns to produce a slightly more "denoised" xt-1 from Zt- Ho et al. 311 parameterize this model using a function cạ(x,, t) which predicts the noise component of noisy sample 24- To train this function, each sample in a minibatch is produced by randomly drawing a data sample Zg. a timestep t,, and noise c, which together give rise to noised sample 2/, (Equation 3 Appendix C). The training objective is then [[cg(Zr, t) - c i.e. a simple mean-squared error loss between the true noise and the predicted noise (Equation 12
Appendix C).
Ho al. 331 show that, under reasonable assumptions, we can then model the denoising distribution
Pa( (z) of æ given as a diagonal Gaussian N (x;-11 juo (are, l), Eo ()), where the mean
(Zr, [Z t) can be calculated as a function of cø t) (Equation 13 Appendix Cp. Ho et al. [ observe that the simple mean-squared error objective, Liimple works better in practice than the actual variational lower bound Lvb that can be derived from interpreting the denoising diffusion model as VAE. They also note that training with this objective and using their corresponding sampling procedure is equivalent to the denoising score matching model from Song and Ermon (65) who use Langevin dynamics to sample from denoising model trained with multiple noise levels to produce high quality image samples. We often use "diffusion models" as shorthand to refer to both classes of models.
Following the breakthrough work of [ong and Ermon papers have proposed improvements to diffusion models. Nichol and Dhariwal 49
65 and Ho et al.
several recent
find that fixing
2

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the variance Eg(r,, t) to a constant as done in Ho et al. [1] is sub-optimal for sampling with fewer diffusion steps, and propose to parameterize [ t) as a neural network whose output is Appendix C are the variances in Ho et al. 31 corresponding to upper and lower bounds for the reverse process variances. Additionally, Nichol and Dhariwal 49 propose a hybrid objective for training both (z f) and Eg(x,, tt) using the weighted sum simple ALvb. Learning the reverse process variances with their hybrid objective allows sampling with fewer steps without much drop in sample quality. We adopt this objective and parameterization, and use it throughout our experiments.
interpolated as (x t) = exp( y log 3r + (1 - v) log Br) Here, 3. and B. (Equation 5
Song et al.
propose DDIM, which formulates an alternative non- Markovian noising process that has the same forward marginals as DDPM, but allows producing different reverse samplers by changing the variance of the reverse noise. By setting this noise to 0, they provide a way to turn any model (I t) into a deterministic mapping from latents to images, and find that this provides an alternative way to sample with fewer steps. We adopt this sampling approach when using fewer than 50 sampling steps, since Nichol and Dhariwal 44 found it to be beneficial in this regime.
Sample Quality Metries:
For comparing sample quality across models, we perform quantitative evaluations using the following metrics. While these metrics are often used in practice and correspond well with human judgement, they are not a perfect proxy, and finding better metries for sample quality evaluation is still an open problem.
We use FID 29
our default metric for overall sample quality comparisons it captures both fidelity and diversity and has been the de facto standard metric for state-of-the-art generative models as proxies for separately measuring fidelity and as a metric that better captures spatial relationships than FID, and also include Inception Score (IS) 6 as another proxy for fidelity. When comparing against other methods, we re-compute these metries using public samples or models whenever possible. This for two reasons: first, some papers 33
[3] 64 R 3J. We use Precision and Recall KX
diversity, respectively. We include sFID 48
compare against arbitrary subsets of the training set which are not readily available; and second, subtle implementation differences can affect the resulting FID values [5 For consistent comparisons, we use the full training set as the reference batch [29
8 and evaluate metrics for all models using the same codebase.
3
Architecture Improvements
Ho et al. aclottdd the UNet architecture 158 for diffusion models, which Aellicoeur-Martinee et al.
32 found to substantially improve sample quality over the previous architectures [65] 39 used for denoising score matching. The UNet model uses a stack of residual layers and downsampling convolutions, followed by a stack of residual layers with upsampling convolutions, with skip con- nections connecting the layers with the same spatial size. In addition, they use a global attention layer at the 16x 16 resolution with a single head, and add a projection of the timestep embedding into each residual block. [Sog et al. [67] found that further changes to the UNet architecture improved performance on the CIFAR-I0 10
37 and CelebA-64 440 datasets. We show the same result on ImageNet 128 128, finding that architecture can indeed give substantial boost to sample quality on a much larger and more diverse datasets at higher resolution.
We explore the following architectural changes: increasing depth versus width, holding model size relatively constant; increasing the number of attention heads; using attention at 32x32, 16x 16, and 8x8 resolutions rather than only 16x 16; using the BigGAN g residual block for upsampling and downsampling the activations, following [7]; and finally; rescaling residual connections with 72' following
67
33 34
We train models with the above architecture changes on ImageNet 128 x 128 and compare them on FID, evaluated at two different points of training, in Table D Aside from rescaling residual connections, all of the other modifications improve performance and have a positive compounding effect. On wall-clock (Figure 5 Appendix [ we find that increased depth hurts training time most, so we opt not to use this change in further experiments. We also study other attention configurations that better match the Transformer architecture [72]. We try two configurations: constant attention heads, or constant channels per head. Table shows our results, indicating that more heads or fewer channels per head improves FID. On wall-clock (Figure Appendix A. we see that 64 channels is best so we opt to use 64 channels per head as our default. We note that this choice also better matches modern transformer architectures, and is on par with our other configurations in terms of final FID.
3

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Table Ablation of various architecture changes, evaluated 700K and 1200K iterations
Attention resolutions
BigGAN up'downsample
Rescale reshlock
FID 700K
FID
Channels
Depth
Heads
1200K
160
2
1
16
X
x
15.33
13.21
128
4
-0.21
-0.48
4
-0,54
-0.82
32,16,8
-0.72
-0.66
-1.20
-1.21
0.16
0.25
160
2
4
32,16,8
x
-3.14
-3.00
Table 2: Ablation of attention heads. More heads lower channels per heads both improve FID. The base model was a smaller version of the best model from Table !
Number of heads
Channels per head
FID
14.08
-0.50
-0.97
-1.17
32
-1.36
64
-1.03
128
-1.08
We also experiment with layer 49 that refer to adaptive group normalization (AdaGN), which incorporates the timestep and class embedding into each residual block after group normalization operation (75) similar to adaptive instance norm [3 and FiLM (54] We define this layer as AdaGN(h, y) yss GroupNorm(()) + yb. where l is the intermediate activations of the residual block following the first convolution, and y [u.: yb] is obtained from linear projection of the timestep and class embedding. We had already seen AdaGN improve our earliest diffusion models, and so had included by default in all runs. We explicitly ablate this choice (Table 6 Appendix A. and find that FID becomes worse by 2.02 when we remove the adaptive group normalization layer.
In the rest of the paper, with residual blocks per resolution, multiple heads with 64 channels per head, attention 32, 16 and 8 resolutions, BigGAN residual blocks for up and downsampling, and adaptive group normalization for injecting timestep and class embeddings into residual blocks.
this final improved model architecture
default: variable width
4 Classifier Guidance
In addition to employing well designed architectures, GANs for conditional image synthesis 45
make heavy use of class labels. This often takes the form of class-conditional normalization statisties
20 [4] as well as discriminators with heads explicitly designed to behave like classifiers p(y xr) 46
As further evidence that class information is crucial the success of these models, Lucic et find that it is helpful to generate synthetic labels when working in a label-limited regime. Given this observation for GANs, makes sense to explore different ways to condition diffusion models on class labels. We already incorporate class information into adaptive group normalization layers (Section 3 Here, we explore a different approach: exploiting a classifier p(y|z) to improve a diffusion generator. Sohl-Dickstein et diffusion model can be conditioned using the gradients of a classifier. particular, we can train classifier P& ( (,) f) on noisy images 2t, and then use gradients V,, P (3) to guide the diffusion sampling process towards an arbitrary class label y.
[ and Song al. [67] show way achieve this, wherein pre-trained
For class conditional diffusion sampling, we reproduce the derivation from Sohl- et al. 6% Appendix D.2 For DDIM, we perform a score-based derivation in Appendix D.3 inspired by Song et al.
67 The resulting sampling algorithms we use for guidance are Algorithms and respectively. Both algorithms incorporate class information by adding the gradients of classifier to each sampling step with appropriate step size. In these algorithms, choose the notation

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Algorithm| 1 Classifier guided diffusion sampling, given diffusion model (No(Zz)) Eo(xe) classi-
fier Po(y)an (t)); and gradient scale 8.
Input: class label y, gradient scale 8
Jr <- sample from NO I)
for all from 7 to 1 do
p4, - pa (zz), [x()))
It-1 f sample from N( + sE Va, logps((los), 2)
end for return
Algorithm 2 Classifier guided DDIM sampling, given diffusion model c0(x:), classifier Po(u(z))) and gradient scale
Input: class label y. gradient scale 8
<- sample from (O,
for all from T to 1 do
8 (x
vI ag Vz, log Po (v)æ,)
2t-1 var-1
+ /1 Ō
Vas
end for return 20
Samples from an unconditional diffusion model with classifier guidance to condition on the class "Pembroke Welsh corgi". Using classifier scale 1.0 (left; FID: 33.0) does not produce convincing samples in this class, whereas classifier scale 10.0 (right; FID: 12.0) produces much more class-consistent images.
Figure 2:
(olaa d) (y) and (0(2,, L) eo (are) for brevity, noting that they refer separate functions for each timestep / and at training time the models must be conditioned on the input 1.
To apply classifier guidance to a large scale generative task, train classification models ImageNet. Our classifier architecture is simply the downsampling trunk of the UNet model with an attention pool [55] at the 8x8 layer to produce the final output. We train these classifiers the same noising distribution as the corresponding diffusion model, and also add random crops to reduce overfitting.
In initial experiments with unconditional ImageNet models, we found it necessary to scale the classifier gradients by a constant factor larger than 1. When using scale of 1, we observed that the classifier assigned reasonable probabilities (around 50%) to the desired classes for the final samples, but these samples did not match the intended classes upon visual inspection. Scaling up the classifier gradients remedied this problem, and the class probabilities from the classifier increased to nearly 100%. Figure 2 shows example of this effect. To understand the effect of scaling classifier gradients, note that V. log logp(y) = V, log }p(y|z)", where result, the conditioning process is still theoretically grounded in a re-normalized classifier distribution proportional to ()) When s > 1, this distribution becomes sharper than p(y(æz), since larger values amplified by the exponent. In other words, using larger gradient scale focuses more on the modes of the classifier, which is potentially desirable for producing higher quality (but less diverse) samples.
an arbitrary constant. As
In the above derivations, we assumed that the underlying diffusion model was unconditional, modeling p(z). It is also possible to train conditional diffusion models, p(zly), and use classifier guidance in
5

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Table Effect of classifier guidance on sample quality. Both conditional and unconditional models were trained for 2M iterations on ImageNet x56x256 with batch size 256.
Conditional
Guidance
Scale
FID
sFID
IS
Precision
Recall
X
26.21
6,35
39.70
0.61
0,63
XXY
1.0
33.03
6.99
32.92
0.56
0.65
10.0
12.00
10.40
95,41
0.76
0.44
X
10.94
6.02
100.98
0.69
0.63
/
V
1.0
4.59
5,25
186.70
0.82
0.52
10.0
9.11
10.93
283.92
0.88
0.32
procsion
16
0.9
14-
10
200
0.5
150
0.4
100
gradient scale
gradient
Figure 3: Change in sample quality as we vary scale of the classifier gradients for class-conditional ImageNet 128x x 128 model.
the exact same way. Table 3 shows that the sample quality of both unconditional and conditional models can be greatly improved by classifier guidance. We see that, with high enough scale, the guided unconditional model can get quite close the FID of an unguided conditional model, although training directly with the class labels still helps. Guiding a conditional model further improves FID,
Table 3 also shows that classifier guidance improves precision at the cost of recall, thus introducing trade-off in sample fidelity versus diversity. We explicitly evaluate how this trade-off varies with the gradient scale in Figure 3 We see that scaling the gradients beyond 1.0 smoothly trades off recall (a measure of diversity) for higher precision and IS (measures of fidelity). Since FID and sFID depend on both diversity and fidelity, their best values are obtained an intermediate point. We also compare our guidance with the truncation trick from BigGAN (Figure C Appendix A.2). We find that classifier guidance is strictly better than BigGAN- deep when trading off FID for Inception Score. Less clear cut is the precision/recall trade-off, which shows that classifier guidance is only a better choice up until a certain precision threshold, after which point it cannot achieve better precision.
5 Results
To evaluate our improved model architecture on unconditional image generation, we train separate diffusion models on three LSUN (77 classes: bedroom, horse, and cat. To evaluate classifier guidance, train conditional diffusion models on the ImageNet [59] dataset 128x 128, 256 256, and 512x512 resolution.
Table summarizes our results. ADM refers to our ablated diffusion model, and ADM-G additionally uses classifier guidance. Our diffusion models can obtain the best FID on each task, and the best sFID all but one task. With the improved architecture, we already obtain state-of-the-art image generation on LSUN and ImageNet 64 x6. For higher resolution ImageNet, we observe that classifier guidance allows models substantially outperform the best GANs. These models obtain perceptual quality similar to GANs, while maintaining a higher coverage the distribution as measured by recall, and can even do so using only 25 sampling steps. We also evaluate the computational requirements for training our models (Table 10 Appendix B and find that we can obtain competitive sample quality while using the or less compute than the corresponding BigGAN-deep or StyleGAN2 model.
Figure compares random samples from the best BigGAN-deep model to our guided diffusion model. While the samples are of similar perceptual quality, the diffusion model contains more modes than the GAN, such as zoomed ostrich heads, single flamingos, different orientations of cheeseburgers, and

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Table 4: Sample quality comparison with state-of afrtthe-rrt generative models for each task. LSUN diffusion models are sampled using 1000 steps (see Appendix D ImageNet diffusion models are sampled using 250 steps, except when we use the DDIM sampler with 25 steps. *No BigGAN-deep model was available at this resolution, so we trained our own. Values are taken from previous paper, due to lack of public models samples. Resullts use two-resolution stacks. Results use compute-imtensive classifier rejection sampling.
Model
FID sFID
Prec
Rec
Model
FID
sFID
Prec
Rec
LSUN Bedrooms 256x256
ImageNet 128x
DCTransformer
6.40
6.66
0.44
0.56
BigGAN-deep B
6.02
7.18
0.86
0.35
DDPM AI
4.89
9.07
0.60
0.45
LOGAN! 74
3.36
IDDPM 49
4.24
8.21
0.62
0.46
ADM
5,91
5.09
0.70
0,65
StyleGAN
3
2.35
6.62
0.59
0.48
ADM-G (25 steps)
5.98
7.04
0.78
0.51
ADM (dropout)
1.90
5.59
0.66
0.51
ADM-G
2.97
5.09
0.78
0.59
ImageNet 256
LSUN Horses 256
DCTransformer
36.51
8.24
0.36
0.67
StyleGAN2 3
3.84
6.46
0.63
0.48
VQ-VAE-21 5
31.11
17.38
0.36
0.57
ADM
2.95
5.94
0.69
0.55
VQ-VAF-2 (RS)
57
10
ADM (dropout)
2.57
6.81
0.71
0.55
VQ-GAN: 21
15.97
19.05
0.63
0.58
VQ-GAN (RS)18
21
5.06
7.34
0.79
0.48
IDDPM 40
12.26
5,42
0.70
0.62
LSUN Cats 256x256
SR3 6U
11.30
DDPM 3I
17.1
12.4
0.53
0.48
BigGAN-deep
8
6,95
7.36
0.87
0.28
StyleGAN2
7.25
6.33
0.58
0.43
ADM
10.94
6.02
0.69
0.63
ADM (dropout)
5.57
6.69
0.63
0.52
ADM-G steps)
5.44
5.32
0.81
0.49
ADM-G
4.59
5.25
0.82
0.52
ImageNet 64
ImageNet 512x512
digep
4.06
3.96
0.79
0.48
BigGAN-deep [
8.43
8.13
0.88
0.29
IDDPM 4J
2.92
3.79
0.74
0.62
ADM
23.24
10.19
0.73
0.60
ADM
2.61
3.77
0.73
0.63
ADM-G (25 steps)
8.41
9.67
0.83
0.47
ADM (dropout) 2.07
4.29
0.74
0.63
ADM-G
7.72
6.57
0.87
0.42
tinca fish with no human holding We also check our generated samples for nearest neighbors in the DnceptionV33 feature space in Appendix and we show additional samples in Appendices M
We also compare guidance using two-stage upsampling stack. Nichol and Dhariwal
4 and
Saharia et al. 60 train two-stage diffusion models by combining a low-resolution diffusion model with a corresponding upsampling diffusion model. In this approach, the upsampling model is trained to upsample images from the training set, and conditions on low-resolution images that are concatenated channel-wist to the model input using simple interpolation (e.g. bilinear). During sampling. the low-resolution model produces sample, and then the upsampling model is conditioned on this sample. This greatly improves FID on ImageNet 256x 256, but does not reach the same performance as state-of-the-an models like BigGAN-deep
40
60
as seen in Table
In Table we show that guidance and upsampling improve sample quality along different axes. We use the upsampling stack from Nichol and Dhariwal
49 combined with our architecture improve- ments, which we refer as ADM-U. While upsampling improves precision while keeping a high recall, guidance provides knob to trade off diversity for much higher precision. We achieve the best FIDs by using guidance lower resolution before upsampling to higher resolution, indicating that these approaches complement one another.
6 Related Work
Score based generative models were introduced by Song and Ermon 66 as a way modeling data distribution using its gradients, and then sampling using Langevin dynamics 73 Ho et al. [3] found connection between this method and diffusion models [33) and achieved excellent sample quality by leveraging this connection. After this breakthrough work, many works followed up with
7

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Figure 4:
Samples from BigGAN-deep with truncation 1.0 (FID 6.95, left) vs samples from our diffusion model with guidance (FID 4.59, middle) and samples from the training set (right).
Table 5: Comparing our single, upsampling and classifier guided models. The upsamplers are 64-2256 and 128-512. When combining guidance with upsampling, we only guide the lower resolution model. All models are sampled using 250 sampling steps.
Model
FID
sFID
IS
Prec
Rec
Model
FID
sFID
Prec
Rec
ImageNet 256 256
ImageNet 512x
ADM
10.94
6.02
100.98
0.69
0.63
ADM
23.24
10.19
58.06
0.73
0.60
ADM, ADM-U
7.49
5.13
127.49
0.72
0.63
ADM. ADM-U
9.96
5.62
121.78
0.75
0.64
ADM-G
4.59
5.25
186.70
0.82
0.52
ADM-G
7.72
6.57
172.71
0.87
0.42
ADM-G, ADM-U
3.94
6.14
215.84
0.83
0.53
ADM-G, ADM-U
3.85
5.86
221.72
0.84 0.53
more promising results: Kong et al. 36 and Chen et al. ||| demonstrated that diffusion models
work well for audio: Joltteuu-Martinauu al. 3> found that GAN-like setup could improve samples from these models; Song et al. 67 explored ways to leverage techniques from stochastic
differential equations improve sample quality obtained by score-based models; [Song et proposed methods to improve sampling speed; Nichol and Dhariwal 660 demonstrated promising results on the difficult ImageNet generation task
and Nichol and Dhariwal
40
40
and Saharia al.
using upsampling diffusion models. Also related to diffusion models, and following the work of
Sohl-Dickstein et al.
63 Goyal al. 277 described a technique for learning a model with learned
iterative generation steps, and found that it could achieve good image samples when trained with
likelihood objective.
One missing element from previous work on diffusion models is a way to trade off diversity for fidelity. Other generative techniques provide natural levers for this trade-off. [rock al. X introduced the truncation trick for GANs, wherein the latent vector is sampled from truncated normal distribution. They found that increasing truncation naturally led to a decrease in diversity but an increase in fidelity. More recently, Razavi et al. 5 proposed to use classifier rejection sampling to filter out bad samples from an autoregressive likelihood- based model, and found that this technique improved FID. DeVries et al. [6 found that filtering out low-density regions of the training set improves GAN training performance. Most likelihood-baat based models also allow for now-eemper sampling (,, which provides a natural way to emphasize modes of the data distribution (see Appendix[]]

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Other tikelihood-basee models have been shown to produce 71 and VQ- VQ-VAE-2 [57] are autoregressive models trained on top of quamtized latent codes, greatly reducing the computational resources required to train these models on large images. These models produce diverse and high quality images, but still fall short of GANs without expensive rejection sampling and special metrics to compensate for blurriness. DCTransformer [X] is a related method
image samples. VQ-VAE
which relies on a more intelligent compression scheme. VAEs are another promising class of likelihood-based models, and recent methods such as NVAE [6 and VDVAE 12 have successfully been applied to difficult image generation domains, Energy-based models are another class of 13
tikeihhodd-basee models with rich history [I] challenging, and Xie et al. images from these models. Du and Mordatch T9
Sampling from the EBM distribution is 76 demonstrate that Langevin dynamics can be used to sample coherent further improve upon this approach, obtaining
30
high quality images. More recently, Gaan et al. [24 incorporate diffusion steps into an energy-based model, and find that doing improves image samples from these models.
Other works have controlled generative models with a pre-trained classifier. For example, an emerging body of work 2 53 2 aims to optimize GAN latent spaces for text prompts using pre-trained CLIP [55] models. More similar to our work, [Song et al. [7 uses a classifier to generate class-conditional CIFAR-10 images with diffusion model. In some cases, classifiers can act as stand-alone generative models. For example, Santurkar et
al. 62 demonstrate that robust image classifier can be used as a stand-alone generative model, and Grathwohl et al. [2]] train a model which is jointly classifier and an energy-based model.
7 Limitations and Future Work
While we believe diffusion models are extremely promising direction for generative modeling, they are still slower than GANs at sampling time due to the use of multiple denoising steps (and therefore forward passes). Since our diffusion models are also larger than the competing GAN generators, each forward pass takes anywhere from 5-20 times longer too. A promising direction to reduce this latency gap is Luhman and Luhman 43), who explore way to distill the DDIM sampling process into a single step model. The samples from the single step model are not yet competitive with GANs, but are much better than previous single-step likelihood- -aaeeood--aaed models. Future work in this direction might be able to completely close the sampling speed gap between diffusion models and GANs without sacrificing image quality.
Unlike GANs, Flows, and VAEs, diffusion models do not learn an explicit latent representation. While DDIM provides way to encode images into implicit latent space, it is unclear how semantically meaningful this latent representation is compared to those of other model classes. This could make difficult to use diffusion models for representation learning or image editing applications.
The effectiveness of classifier guidance demonstrates that we can obtain powerful generative models from the gradients of classification function. This could be used to condition an image generator with a text caption using a noisy version of CLIP (55, similar to recent methods that guide GANs using text prompts 23
5 2 Our proposed classifier guidance technique is currently limited to labeled datasets. the future, our method could be extended to unlabeled data by clustering samples to produce synthetic labels 42 or by training discriminative models to use for guidance. This also suggests that large unlabeled datasets could be leveraged the future to pre-train powerful diffusion models that can later be improved by using classifier with desirable properties.
8 Societal Impact
Our proposed technique makes generative models more accessible in terms of compute costs, es- pecially because new classifiers can be trained and used on top of existing high-qualiny diffusion models. While we believe this is generally a benefit of these models, it could also have negative societal implications. For example, cheaper generative models could enable bad actors to generate fake news, propaganda images, or doctored photos. Additionally, the wide-spread deployment of these models could displace jobs in art, graphic design, animation, and photography. One could imagine, however, that democratizing generative models could also have positive impacts in the long run, creating new types of jobs such as generative photo editing. Intentionally deceitful generated

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images are a more direct concern, and detecting and mitigating propaganda and fake news based on generative models an ongoing area of research 3 [
Conclusion
We have shown that diffusion models, class of likelihood-based models with stationary training objective, can obtain better sample quality than state-of-the-art GANs. Our improved architecture is sufficient to achieve this unconditional image generation tasks, and our classifier guidance technique allows us to do so on class-conditional tasks. In the latter case, we find that the scale of the classifier gradients can be adjusted to trade off diversity for fidelity. These guided diffusion models can reduce the sampling time gap between GANs and diffusion models, although diffusion models still require multiple forward passes during sampling. Finally, by combining guidance with upsampling, we can further improve sample quality on high-resolution conditional image synthesis.
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14

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Checklist
Did you include the license to the code and datasets? [No] We were unable find the official license for either ImageNet or LSUN. We do include a license for our released source code.
1. For all authors...
(a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? [Yes]
(b) Did you describe the limitations of your work? [Yes] See Section
(c) Did you discuss any potential negative societal impacts of your work? [Yes] See
Section g
(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
2. If you are including theoretical results...
(a) Did you state the full set of assumptions of all theoretical results? [Yes] See Appendix
(b) Did you include complete proofs of all theoretical results? [Yes] We provide detailed derivations in Appendix D
3. If you ran experiments..
(a) Did you include the code, data, and instructions needed to reproduce the main experi- mental results (either the supplemental material or as a URL)? [Yes] include the source code and instructions for running it.
(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] See Appendix K
(c) Did you report error bars (e.g., with respect to the random seed after running experi- ments multiple times)? [No] Each experiment requires several hundred GPU days to run, so it is quite costly to compute error bars.
(d) Did you include the total amount of compute and the type of resources used (e.g., type
of GPUs, internal cluster, or cloud provider)? [Yes] See Appendix B
4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
(a) If your work uses existing assets, did you cite the creators? [Yes] Our codebase
references the codebase it is forked from 20 31
We also cite PyTorrc [52] which
we use throughout our experiments.
(b) Did you mention the license of the assets? [Yes] A license file is included with the code release.
(c) Did you include any assets either in the supplemental material URL? [Yes]
The code is included in the supplemental material.
(d) Did you discuss whether and how consent was obtained from people whose data you'l 're using/curating? [N/A]
(c) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
5. If you used crowdsourcing conducted research with human subjects...
(a) Did you include the full text of instructions given to participants and screenshots, applicable? [N/A]
(b) Did you describe any potential participant risks, with links Institutional Review Board (IRB) approvals, if applicable? [N/A]
(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]
15


Reviews:
[{"review_id": "mX6GOhlWLA2", "reviewer": "Reviewer_NiCt", "summary": "The authors explore advances in large scale diffusion models for image generation, and with guidance from an image classifier gradient, demonstrate that diffusion models can outperform state of the art GAN models on image synthesis at different resolutions with respect to standard metrics such as Inception Score, FID. The Classifier guidance also offers a trade-off between sample quality and diversity for diffusion models. ", "questions": "", "limitations": "", "rating": 7, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "- The authors take existing diffusion models, and classifier guidance techniques, and along with few architecture modifications motivated from previous works and show that such a combination on large scale can beat state of the art GAN based models. \n- The paper is clearly written and easy to follow. The experiments are well conducted, with detailed ablation studies. \n- The paper can be of significance to the generative modeling community in establishing the capability of large scale likelihood based diffusion models on the challenging task of image generation.\n- Few questions:\n  - I will be interested to compare the degree of memorization of the model as a function of the scale factor of the classifier guidance. \n    The authors do show some handful samples for scale factor 1.0 and 2.5, but it would be nice to use some form of automated \n    metric (e.g. minimum or average min-K Inception distance between each image and dataset). It might be the case, that for some \n    classes, memorization is more likely than other classes. Also what happens at a scale factor of 10, does the model start \n    memorizing at these scale factors?\n  - Did the authors explore the benefit of classifier guidance as a function of classifier's performance on the validation set? In general \n     how strong is the classifier that the authors trained using the UNet backbone? ", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "The authors adequately address the limitations and potential negative societal impact of their work.\n\n", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "3"}, "extra_text": {}}, {"review_id": "TC3-2ORTZyE", "reviewer": "Reviewer_Fjfm", "summary": "This work demonstrates that diffusion models can outperform the state-of-the-art GAN models on image synthesis.  On unconditional image synthesis, the authors find a better architecture through a series of ablations. On conditional tasks (conditioned on class labels), the authors trade off diversity for fidelity using gradients from a classifier the same architecture. ", "questions": "", "limitations": "", "rating": 9, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Originality:\n- Most of the ideas in this paper are not brand new and were proposed by previous work (e.g., classifier guidance). However, the authors put them together and execute them really well. \n\nQuality:\n- The submission is technically sound.\n\nClarity:\n- This paper is well-written. \n\nSignificance:\n- This paper contains a good number of insights on building the state-of-the-art diffusion models for image synthesis.\n- The architecture improvements are significant.\n\nComments:\n\nThe classifier uses the same architecture as the diffusion model. Is there any special reason? Did the authors try different architecture for classifier guidance, e.g., ResNet with time-step embedding?\n\nOverall, this paper provides successful recipes and non-trivial insights for building state-of-the-art diffusion models for image synthesis. I think it is a good paper. I enjoyed reading it.", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "Yes.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "8"}, "extra_text": {}}, {"review_id": "Rc4UUydUmr1", "reviewer": "Reviewer_H51k", "summary": "This work shows that with some architectural changes, classifier guided sampling and comparable compute requirements, diffusion models can achieve state of the art performance in generative image modeling. The paper provides a wealth of empirical data on the performance of diffusion models and how it is influenced by architectural choices and classifier guidance. Ablations on these components lead to FID scores which improve upon GAN based approaches.", "questions": "", "limitations": "", "rating": 7, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "__Significance__\nDiffusion models are a timely topic and a promising approach to generative modeling. The paper mostly builds upon [46] and demonstrates that diffusion models can achieve state-of-the-art FID scores for unconditional image synthesis tasks on LSUN and class-conditional image synthesis tasks on ImageNet. This is mostly achieved based on extensive experiments regarding architecture changes and classifier guidance.\n\n__Presentation__\nThe paper itself is very readable and well structured. It contains the necessary background and is self-contained by providing the model formulation and derivations in the supplementary. Code is included which helps to understand the precise architecture and, potentially, to reproduce results. Unfortunately, I could not find the implementation used to compute FID scores. As pointed out in l.96, implementations of FID evaluations can differ in many subtle ways making comparisons difficult without access to the precise implementation used.\n\n__References__\nThe paper covers many relevant works on improving diffusion models and score based models. However, given the importance of evaluating the performance on class conditional ImageNet modeling, the related works in this area should be covered more completely. In particular, Esser et al. \"Taming Transformers for High-Resolution Image Synthesis.\" also rely on a more intelligent compression scheme like DCTransformer [45] and report better results, Devries et al. \"Instance Selection for GANs.\" also greatly reduce the computational resources while maintaining performance of BigGAN [8], and Fauw et al. \"Hierarchical Autoregressive Image Models with Auxiliary Decoders.\" use a hierarchical approach related to the upsampling approach used in [46] and [56].\n\n__Strengths__\n- The paper demonstrates very impressive generative performance of diffusion models on a variety of datasets and resolutions.\n- It provides evidence that diffusion models can be scaled to complex and high-resolution image synthesis tasks.\n- It provides a wealth of useful empirical data on the influence of architectural changes and classifier guidance (and its scale) on the performance of diffusion models.\n\n__Weaknesses__\n- The paper contains no methodological novelty. The architecture and training mostly follow [46] (and [8,63] regarding the residual block); classifier guidance follows [59].\n- It provides limited additional insights. [46] already demonstrated improved performance of diffusion models over BigGAN on ImageNet at resolution 64x64, and even how performance improves in a predictable manner with increasing model sizes. The only additional insights over [46] are thus that (i) performance can be further increased with hyperparameter search regarding the architecture and the additional use of classifier guidance, and (ii) the same holds for higher resolutions.\n\n__Comments and Suggestions__\n- Will the pre-trained models be released? Given that the compute resources that went into training the models is one of the main contributions of this work, and the fact that there are still many questions to be explored for diffusion models, availability of these models would increase the significance of this work to other researchers and lead to further progress.\n- l.14: What exactly is the ability to generate \"infinite\" high-quality synthetic images?\n- l.62: sqaured -> squared\n- l.98: It would be helpful to provide the code used for FID evaluation so future works do not run into the same issue of subtle differences which requires re-evaluation of previous works and becomes impossible if neither models or samples are available.\n- l.103: colvolutions -> convolutions\n- l.636: how is the class for the interpolated latents choosen when decoding them?\n\n__Rating__\nOverall, I think that the results are impressive and that the work will serve as an important reference on what is achievable with diffusion models. On the other hand, the work provides rather limited novelty and insights on diffusion models beyond previous works such as [46] which leads to my rating of a weak accept.\n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "Limitations regarding sampling speed and the applicability of classifier guidance to unlabeled datasets are addressed and general, potential societal impacts of generative models are discussed.\nAnother important limitation that could be discussed is the applicability of diffusion models to image modifications and representations. For example, GANs provide a low-dimensional, well-behaved latent code that can be directly decoded to an image. This provides ways to modify and optimize such codes. While the DDIM sampling process provides a way to obtain a latent code with diffusion models, the interpolations shown in the supplementary look worse than those obtained by BigGAN. Similarly, optimizing these latent codes with respect to some desired image outcome is probably infeasible due to the need to run a large number of forward passes. Another simple and interesting experiment would be to decode the same latent code under different class conditionings to see if the latent code captures class-agnostic information (such as pose etc.) similar to BigGAN.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "8"}, "extra_text": {}}, {"review_id": "NsvkBeYEEEK", "reviewer": "Reviewer_rkcu", "summary": "The authors demonstrate that through architectural improvements, diffusion models can achieve state-of-the-art image sample quality, beating previous GANs that have dominated the image generation task for years. They also demonstrate that the sample quality can be further improved post-training using classifier guidance [1,2].\n\n[1] Deep unsupervised learning using nonequilibrium thermodynamics (Sohl-Dickstein et al. 2015)  \n[2] Score-based generative modeling through stochastic differential equations (Song et al. 2020)\n\n", "questions": "", "limitations": "", "rating": 7, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "The main focus of the paper is demonstrating the capabilities of diffusion models for image synthesis. The paper does a great job at conveying this message and is very clearly written. It is interesting to see that after less than a year of research interest around diffusion models, they can beat GANs which have dominated the image synthesis task for years.\n\nThe experiments are strong, containing an ablation study on the neural architecture, a study on the effect of classifier guidance on sample quality, as well as a larger-scale study using metrics beyond just FID, including sFID [2] and Precision and Recall [3] where state-of-the-art performance is demonstrated on several image datasets. \n\nIn terms of technical innovation, the paper has few contributions. The differences compared to [1] are mostly about scaling up parts of the model and using previously proposed changes, which is studied in the ablation study. This is however fine as it is not the main focus of the paper.\n\nOne point of potential improvement could be to include a short discussion / a column in Table 1 on the demands on computation/memory/parameter count as various model components are ablated.\n\n[1] Improved Denoising Diffusion Probabilistic Models (Nichol & Dhariwal, 2020)  \n[2] Generating images with sparse representations (Nash et al., 2021)  \n[3] Improved Precision and Recall Metric for Assessing Generative Models (Kynkäänniemi et al., 2019)", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "Limitations and Societal Impacts are adequately discussed in Sections 7 and 8, respectively.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "3"}, "extra_text": {}}]

Author rebuttal:

Meta-review: All reviewers agree that this is a well-written paper with strong experiments that provide non-trivial insights and results in state-of-the-art diffusion models for image synthesis. The evaluation goes beyond prior work in terms of evaluating sFID, Precision-Recall, and perorming several ablations on neural architecture and the impact of classifier guidance on sample quality. While there were some concerns around the novelty of proposed methods, the careful experiments and strong empirical results in this paper helps to advance the capabilities of generative image models in an impressive fashion.
Decision: Accept (Spotlight)