Original: Classiﬁer-Free Diffusion Guidance
Revised: Classiﬁer-Free Diffusion Guidance

Original: Anonymous Author(s)

Original: AfﬁliationAddress email

Original: Abstract
Revised: Abstract

Original: Classiﬁer guidance is a recently introduced method to trade off mode coverage andsample ﬁdelity in conditional diffusion models post training, in the same spirit aslow temperature sampling or truncation in other types of generative models.
Revised: Classiﬁer guidance is a recently introduced method to trade off mode coverage and sample ﬁdelity in conditional diffusion models post training, in the same spirit as low temperature sampling or truncation in other types of generative models.

Original: Thismethod combines the score estimate of a diffusion model with the gradient of animage classiﬁer and thereby requires training an image classiﬁer separate from thediffusion model.
Revised: This method combines the score estimate of a diffusion model with the gradient of an image classiﬁer and thereby requires training an image classiﬁer separate from the diffusion model.

Original: We show that guidance can be performed by a pure generativemodel without such a classiﬁer: we jointly train a conditional and an unconditionaldiffusion model and ﬁnd that it is possible to combine the resulting conditionaland unconditional scores to attain a trade-off between sample quality and diversitysimilar to that obtained using classiﬁer guidance.
Revised: We show that guidance can be performed by a pure generative model without such a classiﬁer: we jointly train a conditional and an unconditional diffusion model, and ﬁnd that it is possible to combine the resulting conditional and unconditional scores to attain a trade-off between sample quality and diversity similar to that obtained using classiﬁer guidance.

Original:  Introduction
Revised:  Introduction

Original: Diffusion models have recently emerged as an expressive and ﬂexible family of generative models,delivering competitive sample quality and likelihood scores on image and audio synthesis tasks [14,15, 5, 16,  8].
Revised: Diffusion models have recently emerged as an expressive and ﬂexible family of generative models, delivering competitive sample quality and likelihood scores on image and audio synthesis tasks [15, 16, 5, 17, 8].

Original: These models have delivered audio synthesis performance rivaling the quality ofautoregressive models with substantially fewer inference steps [2, 9], and they have delivered
Revised: These models have delivered audio synthesis performance rivaling the quality of autoregressive models with substantially fewer inference steps [2, 9], and they have delivered

Original: ImageNet generation results outperforming BigGAN-deep [1] and VQ-VAE-2 [11] in terms of FIDscore and classiﬁcation accuracy score [6, 3].
Revised: ImageNet generation results outperforming BigGAN-deep [1] and VQ-VAE-2 [11] in terms of FID score and classiﬁcation accuracy score [6, 3].

Original: Dhariwal and Nichol [3] proposed classiﬁer guidance , a technique to boost the sample quality of adiffusion model using an extra trained classiﬁer.
Revised: Dhariwal and Nichol [3] proposed classiﬁer guidance , a technique to boost the sample quality of a diffusion model using an extra trained classiﬁer.

Original: Using classiﬁer guidance, they generate high ﬁdelity,non-diverse ImageNet samples that match or exceed the Inception scores of truncated BigGAN, andby varying the strength of the classiﬁer gradient, they can trade off Inception score [13] and FIDscore [4] (or precision and recall) in a manner similar to varying the truncation parameter of BigGAN.
Revised: Using classiﬁer guidance, they generate high ﬁdelity, non-diverse ImageNet samples that match or exceed the Inception scores of truncated BigGAN, and by varying the strength of the classiﬁer gradient, they can trade off Inception score [14] and FID score [4] (or precision and recall) in a manner similar to varying the truncation parameter of BigGAN.

Original: Prior to classiﬁer guidance, it was not known how to generate “low temperature” samples from adiffusion model similar to those produced by truncated BigGAN: naive ways of doing so, such asscaling the model score vectors or decreasing the amount of Gaussian noise added during sampling,do not work.
Revised: Prior to classiﬁer guidance, it was not known how to generate “low temperature” samples from a diffusion model similar to those produced by truncated BigGAN: naive ways of doing so, such as scaling the model score vectors or decreasing the amount of Gaussian noise added during sampling, are ineffective.

Original: Classiﬁer guidance resolves this issue but raises more questions: (1) Is it possible toachieve the same effect using a pure generative model without any classiﬁer?
Revised: Classiﬁer guidance resolves this issue but raises more questions.

Original: (2) Is it necessary touse a classiﬁer gradient  to achieve this effect, and is classiﬁer guidance able to boost classiﬁer-basedmetrics such asInception score and FID  score  simply because classiﬁer guidance is adversarial toimage classiﬁers and because classiﬁer gradients have special structure? (3) What is an intuitiveexplanation for what is going on during guided sampling?
Revised: Because classiﬁer guidance mixes a score estimate with a classiﬁer gradient during sampling, classiﬁer-guided diffusion sampling can be interpreted as attempting to confuse an image classiﬁer with a gradient-based adversarial attack. This raises the question of whether classiﬁer guidance is successful at boosting classiﬁer-based metrics such as FID and Inception score (IS) simply because it is adversarial against such classiﬁers.

Revised: Stepping in direction of classiﬁer gradients also bears some resemblance to GAN training, particularly with nonparameteric generators; this also raises the question of whether classiﬁerguided diffusion models perform well on classiﬁer-based metrics because they are beginning to resemble GANs, which are already known to perform well on such metrics.

Original: By presenting and analysing classiﬁer-free guidance , we provide some answers to these questions.
Revised: To resolve these questions, we present classiﬁer-free guidance , our guidance method which avoids any classiﬁer entirely.

Revised: Rather than sampling in the direction of the gradient of an image classiﬁer, our method instead mixes the score estimates of a conditional diffusion model and a jointly trained unconditional diffusion model.

Revised: By sweeping over the mixing weight, we attain a FID/IS tradeoff similar to that attained by classiﬁer guidance.

Revised: Our results demonstrate that pure generative diffusion models are capable of synthesizing extremely high ﬁdelity samples possible with other types of generative models.

Original:  Background
Revised:  Background

Original: Let x be data drawn from a data distribution p ( x ) .
Revised: Let x be data drawn from a data distribution p ( x ) .

Original: We train a diffusion model in continuoustime [16, 2, 8]: letting z = { z λ | λ ∈ [ λ min , λ max ] } for hyperparameters λ min < λ max ∈ R , the forward process q ( z | x ) is the variance-preserving Markov process [14] speciﬁed as
Revised: We train a diffusion model in continuous time [17, 2, 8]: letting z = { z λ | λ ∈ [ λ min , λ max ] } for hyperparameters λ min < λ max ∈ R , the forward process q ( z | x ) is the variance-preserving Markov process [15] speciﬁed as

Original: [Equation]
Revised: [Equation]

Original: , whereα
Revised: , where

Original: [Equation]
Revised: [Equation]

Original: We will use the notation p ( z ) (or p ( z λ ) ) to denote the marginal of z (or z λ ) when x ∼ p ( x ) .
Revised: We will use the notation p ( z ) (or p ( z λ ) ) to denote the marginal of z (or z λ ) when x ∼ p ( x ) .

Original: Notethat λ
Revised: Note that λ

Original: = log α 2 λ
Revised: = log α 2 λ

Original: /σ 2 λ , so λ can be interpreted as the log signal-to-noise ratio of z λ , and the forwardprocess runs in the direction of decreasing λ .
Revised: /σ 2 λ , so λ can be interpreted as the log signal-to-noise ratio of z λ , and the forward process runs in the direction of decreasing λ .

Original: Conditioned on x , the forward process can be describedin reverse by the transitions q ( z λ (cid:48) | z λ , x ) =
Revised: Conditioned on x , the forward process can be described in reverse by the transitions q ( z λ (cid:48) | z λ , x ) =

Original: N (˜ µ 
Revised: N (˜ µ λ

Original: [Equation]
Revised: [Equation]

Original: | λ ( z λ , x ) , ˜ 
Revised: | λ ( z λ , x ) , ˜ σ 2 λ

Original: [Equation]
Revised: [Equation]

Original: | λ I ) , where
Revised: | λ I ) , where

Original: [Equation]
Revised: [Equation]

Original: The reverse process generative model p θ ( z ) starts from p
Revised: The reverse process generative model p θ ( z ) starts from p

Original: θ ( z λ min ) =
Revised: θ ( z λ min ) =

Original: N ( 0 , I ) .
Revised: N ( 0 , I ) .

Original: We specify thetransitions:
Revised: We specify the transitions:

Original: [Equation]
Revised: [Equation]

Original: During sampling, we apply this transition along an increasing sequence λ min =
Revised: During sampling, we apply this transition along an increasing sequence λ min =

Original: λ 1 < · · · < λ T =λ max for T timesteps.
Revised: λ 1 < · · · < λ T = λ max for T timesteps.

Original: If the model x θ is correct, then as T → ∞ , we obtain samples from an SDEwhose sample paths are distributed as p ( z ) [16].
Revised: If the model x θ is correct, then as T → ∞ , we obtain samples from an SDE whose sample paths are distributed as p ( z ) [17].

Original: The variance is a log-space interpolation of ˜ σ 2 λ (cid:48) | λand σ 2 λ | λ (cid:48) as suggested by [10]; for simplicity we use a constant hyperparameter v rather than learnedz λ -dependent v .
Revised: The variance is a log-space interpolation of ˜ σ 2 λ (cid:48) | λ and σ 2 λ | λ (cid:48) as suggested by [10]; for simplicity we use a constant hyperparameter v rather than learned z λ -dependent v .

Original: Note that variances simplify to ˜ σ 2 λ (cid:48) | λ as λ (cid:48)
Revised: Note that variances simplify to ˜ σ 2 λ (cid:48) | λ as λ (cid:48)

Original: → λ , so v has an effect only whensampling with non-inﬁnitesimal timesteps as done in practice.
Revised: → λ , so v has an effect only when sampling with non-inﬁnitesimal timesteps as done in practice.

Original: The reverse process mean comes from an estimate x θ ( z λ )
Revised: The reverse process mean comes from an estimate x θ ( z λ )

Original: ≈ x plugged into q ( z λ (cid:48) | z λ , x ) [5, 8] ( x θalso receives λ as input, but we suppress this to keep our notation clean).
Revised: ≈ x plugged into q ( z λ (cid:48) | z λ , x ) [5, 8] ( x θ also receives λ as input, but we suppress this to keep our notation clean).

Original: We parameterize x θ interms of (cid:15) -prediction [5]: x θ ( z λ ) =
Revised: We parameterize x θ in terms of (cid:15) -prediction [5]: x θ ( z λ ) =

Original: ( z λ − σ λ (cid:15) θ ( z λ )) /α
Revised: ( z λ − σ λ (cid:15) θ ( z λ )) /α

Original: λ , and we train on the objective
Revised: λ , and we train on the objective

Original: [Equation]
Revised: [Equation]

Original: [Equation]

Original:  where (cid:15) ∼ N ( 0 , I ) , z λ =α
Revised: (5) where (cid:15) ∼ N ( 0 , I ) , z λ =

Original:  λ x + σ λ (cid:15) , and λ is drawn from a distribution p ( λ ) over [ λ min , λ max ] .
Revised: α λ x + σ λ (cid:15) , and λ is drawn from a distribution p ( λ ) over [ λ min , λ max ] .

Original: This objective is denoising score matching [17] over multiple noise scales [15], and when p ( λ ) isuniform, the objective is proportional to the variational lower bound on the marginal log likelihood ofthe latent variable model (cid:82) p θ ( x | z ) p θ ( z ) d z , ignoring the term for the unspeciﬁed p θ ( x | z ) and forthe prior at z λ min [8].
Revised: This objective is denoising score matching [18] over multiple noise scales [16], and when p ( λ ) is uniform, the objective is proportional to the variational lower bound on the marginal log likelihood of the latent variable model (cid:82) p θ ( x | z ) p θ ( z ) d z , ignoring the term for the unspeciﬁed p θ ( x | z ) and for the prior at z λ min [8].

Original: For a different distribution p ( λ ) , the objective can be interpreted as weightedvariational lower bound whose weighting can be tuned for sample quality [5].
Revised: For a different distribution p ( λ ) , the objective can be interpreted as weighted variational lower bound whose weighting can be tuned for sample quality [5].

Original: We use a p ( λ ) inspiredby the cosine noise schedule of [10]: sampling λ is given by λ = − 2 log tan ( au + b ) for uniformlydistributed u ∈ [0 , 1] , where b = arctan( e − λ max / 2 ) and a = arctan( e − λ min / 2 ) − b .
Revised: We use a p ( λ ) inspired by the cosine noise schedule of [10]: sampling λ is given by λ = − 2 log tan( au + b ) for uniformly distributed u ∈ [0 , 1] , where b = arctan( e − λ max / 2 ) and a = arctan( e − λ min / 2 ) − b .

Original: This representsa hyperbolic secant distribution modiﬁed to be supported on a bounded interval.
Revised: This represents a hyperbolic secant distribution modiﬁed to be supported on a bounded interval.

Original: For ﬁnite timestepsampling, we use λ values corresponding to uniformly spaced u ∈ [0 , 1] .
Revised: For ﬁnite timestep sampling, we use λ values corresponding to uniformly spaced u ∈ [0 , 1] .

Original: Because the loss for (cid:15) θ ( z λ ) is denoising score matching for all λ , the score (cid:15) θ ( z λ ) learned by ourmodel estimates the gradient of the log-density of the distribution of our noisy data z λ , that is (cid:15)  ( z λ ) ≈σ λ ∇ z λ log p ( z λ )  .
Revised: Because the loss for (cid:15) θ ( z λ ) is denoising score matching for all λ , the score (cid:15) θ ( z λ ) learned by our model estimates the gradient of the log-density of the distribution of our noisy data z λ , that is (cid:15) θ ( z λ ) ≈ − σ λ ∇ z λ log p ( z λ ) ; note, however, that because we use unconstrained neural networks to deﬁne (cid:15) θ , there need not exist any scalar potential whose gradient is (cid:15) θ .

Original: Sampling from the learned diffusion model resembles using Langevin diffusion tosample from a sequence of distributions p ( z λ ) that converges to the conditional distribution p ( x ) ofthe original data x .
Revised: Sampling from the learned diffusion model resembles using Langevin diffusion to sample from a sequence of distributions p ( z λ ) that converges to the conditional distribution p ( x ) of the original data x .

Original: In the case of conditional generative modeling, the data x is drawn jointly with conditioning information c , i.e. a class label for class-conditional image generation.
Revised: In the case of conditional generative modeling, the data x is drawn jointly with conditioning information c , i.e. a class label for class-conditional image generation.

Original: The only modiﬁcation to the model isthat the reverse process function approximator receives cas input, as in (cid:15) θ ( z λ , c ) .
Revised: The only modiﬁcation to the model is that the reverse process function approximator receives c

Original:  Guidance
Revised:  Guidance

Original: An interesting property of certain generative models, such as GANs and ﬂow-based models, is theability to perform truncated or low temperature sampling by decreasing the variance or range of noiseinputs to the generative model at sampling time.
Revised: An interesting property of certain generative models, such as GANs and ﬂow-based models, is the ability to perform truncated or low temperature sampling by decreasing the variance or range of noise inputs to the generative model at sampling time.

Original: The intended effect is to decrease the diversity ofthe samples while increasing the quality of each individual sample.
Revised: The intended effect is to decrease the diversity of the samples while increasing the quality of each individual sample.

Original: Truncation in BigGAN [1], forexample, yields a tradeoff curve between FID score and Inception score for low and high amounts oftruncation, respectively.
Revised: Truncation in BigGAN [1], for example, yields a tradeoff curve between FID score and Inception score for low and high amounts of truncation, respectively.

Original: Low temperature sampling in Glow [7] has a similar effect.
Revised: Low temperature sampling in Glow [7] has a similar effect.

Original: 3.1 Classiﬁer guidance

Original: Unfortunately, straightforward attempts of implementing truncation or low temperature samplingin diffusion models are ineffective.
Revised: Unfortunately, straightforward attempts of implementing truncation or low temperature sampling in diffusion models are ineffective.

Original: For example, scaling model scores or decreasing the varianceof Gaussian noise in the reverse process cause the diffusion model to generate blurry, low qualitysamples [3]. 
Revised: For example, scaling model scores or decreasing the variance of Gaussian noise in the reverse process cause the diffusion model to generate blurry, low quality samples [3]. 3.1 Classiﬁer guidance

Original: To obtain a truncation-like effect in diffusion models, Dhariwal and Nichol [3] introduce classiﬁerguidance , where the diffusion score (cid:15) θ ( z λ , c )
Revised: To obtain a truncation-like effect in diffusion models, Dhariwal and Nichol [3] introduce classiﬁer guidance , where the diffusion score (cid:15) θ ( z λ , c )

Original: ≈  σ λ ∇ z λ log p ( z λ | c ) is modiﬁed to include thegradient of the log likelihood of an auxiliary classiﬁer model p θ ( c |
Revised: ≈ − σ λ ∇ z λ log p ( z λ | c ) is modiﬁed to include the gradient of the log likelihood of an auxiliary classiﬁer model p θ ( c |

Original: z λ ) as follows:
Revised: z λ ) as follows:

Original: [Equation]
Revised: [Equation]

Original: where w is a parameter that controls the strength of the classiﬁer guidance.
Revised: where w is a parameter that controls the strength of the classiﬁer guidance.

Original: This modiﬁed score˜ (cid:15) θ ( z λ , c ) is then used in place of (cid:15) θ ( z λ , c ) when sampling from the diffusion model, which has theeffect of up-weighting the probability of data for which the classiﬁer p
Revised: This modiﬁed score ˜ (cid:15) θ ( z λ , c ) is then used in place of (cid:15) θ ( z λ , c ) when sampling from the diffusion model, which has the effect of up-weighting the probability of data for which the classiﬁer p

Original: θ ( c | z λ ) assigns high likelihoodto the correct label: data that can be classiﬁed well scores high on the Inception score of perceptualquality [13], which rewards generative models for this by design.
Revised: θ ( c | z λ ) assigns high likelihood to the correct label: data that can be classiﬁed well scores high on the Inception score of perceptual quality [14], which rewards generative models for this by design.

Original: Dhariwal and Nichol [3] thereforeﬁnd that by setting w > 0 they can improve the Inception score of their diffusion model, at theexpense of decreased diversity in their samples.
Revised: Dhariwal and Nichol [3] therefore ﬁnd that by setting w > 0 they can improve the Inception score of their diffusion model, at the expense of decreased diversity in their samples.

Original: Interestingly, they obtain their best results whenapplying classiﬁer guidance to an already class-conditional model as described above, and they ﬁndthat applying guidance to an unconditional model performs less well: the effects of class-conditioningand guidance thus seem complimentary.
Revised: Interestingly, they obtain their best results when applying classiﬁer guidance to an already class-conditional model as described above, and they ﬁnd that applying guidance to an unconditional model performs less well: the effects of class-conditioning and guidance thus seem complimentary.

Original: 3.2 Classiﬁer-free guidance
Revised: 3.2 Classiﬁer-free guidance

Original: A downside of classiﬁer guidance is that it requires an additional classiﬁer model and thus complicatesthe training pipeline.
Revised: A downside of classiﬁer guidance is that it requires an additional classiﬁer model and thus complicates the training pipeline.

Original: This model has to be trained on noisy data z λ , so it is not possible to plugin a standard pre-trained classiﬁer.
Revised: This model has to be trained on noisy data z λ , so it is not possible to plug in a standard pre-trained classiﬁer.

Original: We explore an alternative method of modifying (cid:15) θ ( z λ , c ) toachieve the same effect of boosting the perceptual quality as measured by the Inception score withoutrequiring an auxiliary classiﬁer.
Revised: We explore an alternative method of modifying (cid:15) θ ( z λ , c ) to achieve the same effect of boosting the perceptual quality as measured by the Inception score without requiring an auxiliary classiﬁer.

Original: We call this new method classiﬁer-free guidance .
Revised: We call this new method classiﬁer-free guidance .

Original: Instead of training a separate classiﬁer model, we choose to train an unconditional denoising diffusionmodel p θ ( z ) parameterized through a score estimator (cid:15) θ ( z λ ) together with the conditional modelp θ ( z | c ) parameterized through (cid:15)
Revised: Instead of training a separate classiﬁer model, we choose to train an unconditional denoising diffusion model p θ ( z ) parameterized through a score estimator (cid:15) θ ( z λ ) together with the conditional model p θ ( z | c ) parameterized through (cid:15)

Original: θ ( z λ , c ) .
Revised: θ ( z λ , c ) .

Original: We use a single neural network to parameterize bothmodels, where for the unconditional model we can simply input zeros for the class identiﬁer c whenpredicting the score, i.e. (cid:15) θ ( z λ ) =
Revised: We use a single neural network to parameterize both models, where for the unconditional model we can simply input zeros for the class identiﬁer c when predicting the score, i.e. (cid:15) θ ( z λ ) =

Original: (cid:15) θ ( z λ , c = 0 ) .
Revised: (cid:15) θ ( z λ , c = 0 ) .

Original: We jointly train the unconditional and conditionalmodels simply by randomly setting c to the unconditional class identiﬁer.
Revised: We jointly train the unconditional and conditional models simply by randomly setting c to the unconditional class identiﬁer.

Original: Wecan then apply Bayes’ rule to obtain an implicit classiﬁer as p iθ ( c | z λ ) ∝ p θ ( z λ | c ) /p
Revised: We then perform sampling using the following linear combination of the conditional and unconditional score estimates: [Equation]

Original:  θ ( z λ ) .
Revised: Eq. (6) has no classiﬁer gradient present, so taking a step in the ˜ (cid:15) θ direction cannot be interpreted as a gradient-based adversarial attack on an image classiﬁer. Furthermore, ˜ (cid:15) θ is constructed from score estimates that are non-conservative vector ﬁelds due to the use of unconstrained neural networks, so there in general cannot exist a scalar potential such as a classiﬁer log likelihood for which ˜ (cid:15) θ is the classiﬁer-guided score. Despite the fact that there in general cannot exist a classiﬁer for which Eq.

Original: Thescore of this implicit classiﬁerwill then be given by ∇ z λ log p iθ ( c | z 
Revised: (6) is the classiﬁerguided score, it is in fact inspired by the gradient of an implicit classiﬁer p i ( c | z λ ) ∝ p ( z λ | c ) /p

Original:  λ ) 
Revised: ( z λ ) .

Original: ≈ 1 σ λ 
Revised: If we had access to exact scores (cid:15) ∗ ( z λ , c ) and (cid:15) ∗ ( z λ ) (of p ( z λ | c ) and p ( z λ ) , respectively), then the gradient of this implicit classiﬁer would be ∇ z λ log p i ( c | z λ ) = − 1 σ λ [ (cid:15) ∗ ( z λ , c ) − (cid:15) ∗ ( z λ )] , and classiﬁer guidance with this implicit classiﬁer would modify the score estimate into ˜ (cid:15) ∗ ( z λ , c ) =

Original: [ (cid:15) θ ( z λ , c ) −  (cid:15) θ ( z λ )] .
Revised: (1 + w ) (cid:15) ∗ ( z λ , c ) − w (cid:15) ∗ ( z λ ) .

Original: Applying classiﬁer guidance with this implicit classiﬁer yields the following modiﬁcation to thediffusion score estimator: [Equation]
Revised: Note the resemblance to Eq.

Original: We then use ˜ (cid:15) θ ( z λ , c ) to sample from our diffusion model as usual, thus producing approximatesamples from ˜ p θ ( z λ | c ) ∝ p θ ( z λ | c ) p iθ (  c |
Revised: (6), but also note that (cid:15) ∗ ( z λ , c ) differs fundamentally from (cid:15) θ ( z λ , c ) . The former is constructed from the scaled classiﬁer gradient (cid:15) ∗ ( z λ , c ) − (cid:15) ∗ ( z λ ) ; the latter is constructed from the estimate (cid:15) θ ( z λ , c ) − (cid:15) θ ( z λ ) , and this expression is not in general the (scaled) gradient of any classiﬁer, again because the score estimates are the outputs of unconstrained neural networks.

Original: z λ ) w .
Revised: The fact that Eq. (6) is as effective as classiﬁer guidance despite this is an empirical ﬁnding that we report in Section 4.

Original:  Experiments
Revised:  Experiments

Revised: Our method is extremely simple to implement: during training we simply drop out the class label, and during sampling we simply mix the conditional and unconditional scores as in Eq.

Original: We apply our proposed classiﬁer-free guidance to 64 × 64 area-downsampled ImageNet [12].
Revised: Here, we report our results on 64 × 64 area-downsampled ImageNet [12].

Original: Wetrained a model with architecture and hyperparameters identical to the 64 × 64 model in [3], and wejointly trained the model on unconditional generation with probability 0.1.
Revised: We trained a model with architecture and hyperparameters identical to the 64 × 64 model in [3], and we jointly trained the model on unconditional generation with probability 0.1.

Original: We choose λ min = − 20 ,λ max = 20 , and v = 0 .
Revised: We choose λ min = − 20 , λ max = 20 , and v = 0 .

Original: We consider implied-classiﬁer weights w ∈ { 0 , 0 . 1 , 0 . 2 , . .
Revised: We consider implied-classiﬁer weights w ∈ { 0 , 0 . 1 , 0 . 2 , . .

Original: , 5 } andcalculate FID and Inception Scores with 50000 samples for each value using T = 256 sampling steps.
Revised: , 5 } and calculate FID and Inception Scores with 50000 samples for each value using T = 256 sampling steps.

Original: Figure 1 and Fig.
Revised: Figure 1 and Fig.

Original: 2 list our results: we obtain the best FID result with a small amount of guidance( w = 0 . 1 ) and the best IS result with strong guidance ( w ≥ 4 ).
Revised: 2 list our results: we obtain the best FID result with a small amount of guidance ( w = 0 . 1 ) and the best IS result with strong guidance ( w ≥ 4 ).

Original: These results compare favorablyto [3, 6] and are currently state-of-the-art for this data set as far as we are aware for models thatuse T ≈ 256 steps (the ADM result uses 250 steps, and the CDM result is a two-stage model with4000 steps each).
Revised: These results compare favorably to [3, 6] and are currently state-of-the-art for this data set as far as we are aware for models that use T ≈ 256 steps (the ADM result uses 250 steps, and the CDM result is a two-stage model with 4000 steps each).

Original: Between these two extremes we see a clear trade-off between these two metrics of perceptual quality, with FID monotonically decreasing and IS monotonically increasing withguidance weight w .
Revised: Between these two extremes we see a clear trade-off between these two metrics of perceptual quality, with FID monotonically decreasing and IS monotonically increasing with guidance weight w .

Original: Figure 3 shows randomly generated samples from our model for different levels of guidance: herewe clearly see that increasing guidance has the effect of decreasing sample variety and increasingindividual sample ﬁdelity. 
Revised: Figure 3 shows randomly generated samples from our model for different levels of guidance: here we clearly see that increasing guidance has the effect of decreasing sample variety and increasing individual sample ﬁdelity. Figure 4 shows samples from a similar model trained on 128 × ImageNet.

Original: Method
Revised: Method

Original: FID ( ↓ )
Revised: FID ( ↓ )

Original: IS ( ↑ )
Revised: IS ( ↑ )

Original: ADM [3] 2.
Revised: ADM [3] 2.

Original: CDM [6] 1.
Revised: CDM [6] 1.

Original: Ours, no guidance 1.
Revised: Ours, no guidance 1.

Original: Ours, with guidance w = 0 .1.
Revised: Ours, with guidance w = 0 .1.

Original: w = 0 .2.
Revised: w = 0 .2.

Original: w = 0 .3.
Revised: w = 0 .3.

Original: w = 0 .4.
Revised: w = 0 .4.

Original: w = 0 .5.
Revised: w = 0 .5.

Original: w = 0 .7.
Revised: w = 0 .7.

Original: w = 0 .8.
Revised: w = 0 .8.

Original: w = 

Revised: w =

Original: w = 0 .11.
Revised: w = 0 .11.

Original: w = 1 .12.
Revised: w = 1 .12.

Original: w = 2 .21.
Revised: w = 2 .21.

Original: w = 3 .24.
Revised: w = 3 .24.

Original: w = 4 .26.
Revised: w = 4 .26.

Original: FID
Revised: FID

Original: I S
Revised: I S

Revised: [Figure]

Revised: Interestingly, strongly guided samples such as these display saturated colors.

Original:  Conclusion
Revised:  Discussion

Original: Returning to the questions we posed in the introduction: since  classiﬁer-free guidance is able to tradeoff IS and FID like classiﬁer guidance without needing an extra trained classiﬁer,  we have resolvedour question of whether guidance can be performed with a pure generative model.
Revised: The most practical advantage of our classiﬁer-free guidance method is its extreme simplicity: it is only a one-line change of code during training—to randomly drop out the class conditioning—and during sampling—to mix the conditional and unconditional score estimates. Classiﬁer guidance, by contrast, complicates the training pipeline since it requires training an extra classiﬁer. This classiﬁer must be trained on noisy z λ , so it is not possible to plug in a standard pre-trained classiﬁer. Besides practical advantages, classiﬁer-free guidance is able to trade off IS and FID like classiﬁer guidance without needing an extra trained classiﬁer, so we have demonstrated that guidance can be performed with a pure generative model.

Original: We conﬁrm that itis possible to maximize Inception scores using classiﬁer-free guidance (and  FID score for a smallamount of guidance), thus providing evidence that classiﬁer-based sample quality metrics can beimproved using methods that are not adversarial against ImageNet classiﬁers using classiﬁer gradients.
Revised: We conﬁrm that it is possible to maximize Inception scores using classiﬁer-free guidance (and improve FID score for a small amount of guidance), thus providing evidence that classiﬁer-based sample quality metrics can be improved using methods that are not adversarial against ImageNet classiﬁers using classiﬁer gradients.

Revised: Our diffusion models are parameterized by unconstrained neural networks and therefore their score estimates do not necessarily form conservative vector ﬁelds, unlike classiﬁer gradients [13].

Revised: Therefore, an unconditional-guided sampler follows step directions that do not resemble classiﬁer gradients at all and thus cannot be interpreted as a gradient-based adversarial attack on a classiﬁer; hence our results show that boosting the classiﬁer-based IS and FID metrics can be accomplished with pure generative models with a sampling procedure that is not adversarial against image classiﬁers.

Original: Finally also have  an intuitive explanation for what guidance does: it decreases the unconditionallikelihood of the sample while increasing the conditional likelihood.
Revised: We also have arrived at an intuitive explanation for how guidance works: it decreases the unconditional likelihood of the sample while increasing the conditional likelihood.

Original: Our classiﬁer-free guidancedecreases the unconditional likelihood with a negative score term, which to our knowledge has notyet been explored and may ﬁnd uses in other applications.
Revised: Classiﬁer-free guidance accomplishes this by decreasing the unconditional likelihood with a negative score term, which to our knowledge has not yet been explored and may ﬁnd uses in other applications.

Original: A potential disadvantage of classiﬁer-free guidance is sampling speed.
Revised: A potential disadvantage of classiﬁer-free guidance is sampling speed.

Original: Generally, classiﬁers can besmaller and faster than generative models, so classiﬁer guided sampling may be faster than classiﬁerfree guidance because the latter needs to run two forward passes of the diffusion model, one forconditional score and another for the unconditional score.
Revised: Generally, classiﬁers can be smaller and faster than generative models, so classiﬁer guided sampling may be faster than classiﬁerfree guidance because the latter needs to run two forward passes of the diffusion model, one for conditional score and another for the unconditional score.

Original: The necessity to run multiple passes of thediffusion model might be mitigated by changing the architecture to inject conditioning late in thenetwork, but we leave this exploration for future work.
Revised: The necessity to run multiple passes of the diffusion model might be mitigated by changing the architecture to inject conditioning late in the network, but we leave this exploration for future work.

Original: It may be possible to entirely avoid training an unconditional model. If we know the class distributionand there are only a few classes, we can use the fact that (cid:80) c p ( x | c ) p ( c ) = p ( x ) to obtain anunconditional score from conditional scores without explicitly training for the unconditional score. Of course, this would require as many forward passes as possible values of c and would be inefﬁcientfor high dimensional conditioning signals. We have presented a method to increase sample quality while decreasing sample diversity, just likeclassiﬁer guidance.
Revised: Finally, any guidance method that increases sample ﬁdelity at the expense of diversity must face the question of whether decreased diversity is acceptable.

Original: There may be negative impactsof doing so in deployed models, since samplediversity is important to maintain in applications where certain parts of the data are underrepresentedin the context of the rest of the data.
Revised: There may be negative impacts in deployed models, since sample diversity is important to maintain in applications where certain parts of the data are underrepresented in the context of the rest of the data.

Original: It would be an interesting avenue of future work to try to boostsample quality while maintaining sample diversity.[Figure] Checklist
Revised: It would be an interesting avenue of future work to try to boost sample quality while maintaining sample diversity.

Original:  For all authors.. (a) Do the main claims made in the abstract and introduction accurately reﬂect the paper’s contributions and scope? [Yes]
Revised:  Conclusion

Original: (b) Did you describe the limitations of your work?

Original: [Yes]

Original: (c) Did you discuss any potential negative societal impacts of your work? [Yes] (d) Have you read the ethics review guidelines and ensured that your paper conforms tothem? [Yes]
Revised: We have presented classiﬁer-free guidance, a method to increase sample quality while decreasing sample diversity in diffusion models.

Original: If you are including theoretical results... (a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results?
Revised: Classiﬁer-free guidance is classiﬁer guidance without a classiﬁer, and our results showing the effectiveness of classiﬁer-free guidance conﬁrm that pure generative diffusion models are capable of maximizing classiﬁer-based sample quality metrics while entirely avoiding classiﬁer gradients.

Original: [N/A]

Original: If you ran experiments...

Original: (a) Did you include the code, data, and instructions needed to reproduce the main experi-

Original: mental results (either in the supplemental material or as a URL)?

Original: [No] Will be released later. (b) Did you specify all the training details (e g., data splits, hyperparameters,
Revised: We look forward to further explorations of classiﬁer-free guidance in a wider variety of settings.

Original: how they were chosen)? [Yes] (c) Did you report error bars (e
Revised: Acknowledgments and Disclosure of Funding

Original: g., with respect to the random seed after running experi-

Original: ments multiple times)? [No] (d) Did you include the total amount of compute and the type of resources used (e g., type
Revised: We thank Ben Poole and Mohammad Norouzi for feedback.

Original: of GPUs, internal cluster, or cloud provider)?

Original: [Yes]

Original: If you are using existing assets (e

Original: g., code, data, models) or curating/releasing new assets...

Original: (a) If your work uses existing assets, did you cite the creators?

Original: [Yes] We used ImageNet.

Original: (b) Did you mention the license of the assets?

Original: [No] ImageNet is standard.

Original: (c) Did you include any new assets either in the supplemental material or as a URL?

Original: [N/A]

Original: (d) Did you discuss whether and how consent was obtained from people whose data you’re

Original: using/curating?

Original: [N/A]

Original: (e) Did you discuss whether the data you are using/curating contains personally identiﬁable

Original: information or offensive content?

Original: [N/A]

Original: If you used crowdsourcing or conducted research with human subjects...

Original: (a) Did you include the full text of instructions given to participants and screenshots, if

Original: applicable?

Original: [N/A]

Original: (b) Did you describe any potential participant risks, with links to Institutional Review

Original: Board (IRB) approvals, if applicable?

Original: [N/A](c)

Original: Did you include the estimated hourly wage paid to participants and the total amountspent on participant compensation?

Original: [N/A]