Unlearning in Diffusion models under Data Constraints: A Variational Inference Approach
Authors: Subhodip Panda
Varun M S
Shreyans Jain
Sarthak Kumar Maharana
Prathosh AP
Venue: Accepted by TMLR ()

Abstract: For a responsible and safe deployment of diffusion models in various domains, regulating the generated outputs from these models is desirable because such models could generate undesired, violent, and obscene outputs. To tackle this problem, recent works use machine unlearning methodology to forget training data points containing these undesired features from pre-trained generative models. However, these methods proved to be ineffective in data-constrained settings where the whole training dataset is inaccessible. Thus, the principal objective of this work is to propose a machine unlearning methodology that can prevent the generation of outputs containing undesired features from a pre-trained diffusion model in such a data-constrained setting. Our proposed method, termed as Variational Diffusion Unlearning (**VDU**), is a computationally efficient method that only requires access to a subset of training data containing undesired features. Our approach is inspired by the variational inference framework with the objective of minimizing a loss function consisting of two terms: *plasticity inducer* and *stability regularizer*. *Plasticity inducer* reduces the log-likelihood of the undesired training data points, while the *stability regularizer*, essential for preventing loss of image generation quality, regularizes the model in parameter space. We validate the effectiveness of our method through comprehensive experiments for both class unlearning and feature unlearning. For class unlearning, we unlearn some user-identified classes from MNIST, CIFAR-10, and tinyImageNet datasets from a pre-trained unconditional denoising diffusion probabilistic model (DDPM). Similarly, for feature unlearning, we unlearn the generation of certain high-level features from a pre-trained Stable Diffusion model.

Published in Transactions on Machine Learning Research (03/2026)
Unlearning in Diffusion models under Data Constraints: A Variational Inference Approach
Subhodip Panda
subhodipp@iisc.oc.
Deportment of ECE Indian Institate of Science
Varun M
varan.004290mmaillcco com
Department Computer Science PES University
Shreyans Jain Department of EE Indian Institute of Technology, Gandhinagar
shreeaass.jann@Hittmm.cc
Sarthak Kumar Maharana
skm.2000055@uttaaaaas.coooo
Deportment of Computer Science The University of Texas at Dollas
Prathosh A.P
prathosh @tisc.
Deportment of ECE, Indian Institute of Science LatentForce..t at
Reviewed OpenReview: /ttps://openreviite net/ formm? id= mAHRgseyOV
Abstract
For a responsible and safe deployment of diffusion models in various domains, regulating the generated outputs from these models is desirable because such models could generate undesired, violent, and obscene outputs. To tackle this problem, recent works machine unlearning methodology to forget training data points containing these undesired features from pre-trained generative models. However, these methods proved to be ineffective in data-constrained settings where the whole training dataset inaccessible. Thus, the principal objective of this work is to propose machine unlearning methodology that can prevent the generation of outputs containing undesired features from a pre-trained diffusion model in such data-constrained setting. Our proposed method, termed as Variational Diffusion Unlcarning (VDU), is computationally efficient method that only requires access to subset of training data containing undesired features. Our approach is inspired by the variational inference framework with the objective of minimizing a loss function consisting of two terms: plasticity inducer and stability regularizer. Plasticity inducer reduces the log-likelihood of the undesired training data points, while the stability regularizer, essential for preventing loss of image generation quality, regularizes the model in parameter space. We validate the effectiveness our method through comprehensive experiments for both class unlearning and feature unlearning. For class unlearning, unlearn some user-identified classes from MNIST, CIFAR-10, and IinyemageNet datasels from a pre-trained unconditional denoising diff'usion probabilistic model (DDPM). Similarly, for feature unlearning, we unlearn the generation of certain high-level features from a pre-trained Stable Diffusion model trained on the LAION-5B dataset. Our code is publicly available at htttps://giie com Sunm/Sbbhodipp2//DD

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Published in Transactions on Machine Learning Research (03/2026)
(o) Original "0"
(b) Unlearned "0"
(c) Original "froy" (d) Unlearned "froy" (e) Original "bottle" ( Unteorned "bottle"
3
!
5
3
4
8
7
7
1
Unleamiigg Concept "Van_ "Van_Gogh"
Prompt portrait of van gogh"
Original
Unlearned
Unlearned
Unieerned
Unlearned egoch=4
Unlearned egoch=
epach=1
epoch=2
epoch=
Figure 1: (a), (c), and (e) show the original images generated by pre-trained DDPM model on the MNIST, CIFAR-10, and tinylmageNet datasets, respectively. (b), (d) and (f) display the corresponding images generated after unlearning, using our method VDU. The same noise vectors used to generate the original images were applied the unlearned model generate the unlearned images. The latter images show the performance of VDU for unlearning 'Van Gogh' style from Stable Diffusion model. It shown that the model slowly unlearns this artistic style feature unlearning, as well. Additional results on class-unlearning and feature-umleaningg can be found in Figure Figure Figure
multiple epochs. VDU delivers good-quality images after
Figu Figure?
F Figure
g
and Figure I0
1 Introduction
In recent years, diffusion models Dickl-Dickstein et al. 2015; Song & Ermon 2019 Ho 2020 Song
et al. 2021 Rombach et al. 2022) have been popular for generating high-quality images that useful for various tasks such as image and video editing (Ceylan et al. 2023 Feng et al. 2024), text-to-image translation (Ramesh et al. 2021 2022 Saharia et al. 2022) etc. As these models become widespread, there lies a requirement to train them on vast amounts of internet data for diverse and robust output generation. However, there is also a potential downside to using such models, as they often generate outputs containing biased, violent, and obscene features (Tommasi et al. 2017). Thus, a safe and responsible generation from these models becomes an important requirement.
To address these challenges, recent works (Schramowski et al.
2024 Tiwary et al. 2023 have proposed methods for GANs (Goodfellww et al.) 2020), and Diffussin models (Ho et al. 2020 to ensure their safe and responsible deployment, with machine unlearning emerging as a particularly important technique for controlling the safe generation of content develop a computationally efficient method to forget the subset of training data containing these undesired features from the pre-trained model. Thus, ideally, the unlearned model should behave like the retrained model trained without the undesired data subset. However, achieving this goal is challenging because, during the process of unlearning, the model's generalization capacity gets hurt, making the quality of the generated outputs poor. This phenomenon is well studied in a similar context, also known as calastrophic forgelling (McCloskey & Cohen. 1989: Goodfellww et al., 2014 Kirkpatrick et al. 2017 Ginart et al. 2019 Nguyen et al.) (0200) where plasticity to adapt to a new task hurts the stability the model to perform well on the older task had been trained on. In this case, the new task of unlearning an undesired subset of data hurts the quality of images generated by the unlearned model thereafter. Thus, the primary question of unlearning is:
2023 Moon al.
Panda & A.P. 2023 Gandikota et al. 2023a Heng & Soh 2023 Fan et al. 2024
regulating the outputs of various generative models (e.g. VAEs (Kingma 2013
from these models. The key idea of machine unlearning
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Can we develop an algorithm that can forget an undesired subset of training data from pre-trained diffusion model while minimizing the degradalion in generation quality?
To answer this question, a recent unlearning work Selective Amnesia (SA) (Heng & Soh 2023 adopts a continual learning setup and proposes an unlearning method based on elastic weight consolidation (EWC) (Kirk patrick et al., 2017) wherein a weight regularization strategy, in the parameter space, is introduced to balance the unlearning task and to retain the sample quality. In essence, the variation of parameters is penalized by computing the "importance', to retain good performance, using the Fisher Information Matrix (FIM) ([Sagun et al. 2017). However, this unlearning method has two potential downsides: (a) EWC formulation requires the calculation of the FIM, which is expensive due to the gradient product. (b) Tt often generates low-quality samples when it relies solely on the unlearning data subset. To solve the problem of low generation quality, the authors employ a generative replay to retrain the model with generated samples from the "non-unlearning" data subsets, further enhancing computational requirements. Similarly, Saliency Unlearning (SalUn) (Fan et al. 2024) proposes the perturbation of the most influential parameters across the entire model, with the assumption that the complete training dataset is available for reference. A major challenge, however, lies in situations with partial access to the training data due to rising concerns for data privacy and safety (Bac
et al. 2018). In such a case, these methods performs poorly with no access to the non-unlearning data.
Taking note of such crucial observations, our research aims to develop a computationally efficient algorithm for unlearning an undesired class of training data from a pre-trained diffusion model. It also important to mention that our methodology only requires partial access to a subset of training data aimed at unlearning because it is not always feasible to have access to the full training dataset (Chundawat et al.) 2023b Panda et al. 2024). While such realistic setup is challenging, we draw inspiration from works on variational
inference techniques (Nguyen et al. 2018 Noel Loo 2021 Knoblauch et al, 2022 Wild et al. 2022 We propose, Variational Diffusion Unlearning (VDU) algorithm using a variational inference framework in the parameler space, to unlearn a subset of training data. The theoretical formulation of the variational divergence yields a lower bound that is adapted as a loss function to fine-tune the pre-trained model for unlearning. The proposed loss consists of two terms: plasticity inducer and stability regularizer. The plasticity inducer is used for adapting the new task of reducing the log- likelikdd of the unlearning data, while the slabilily regularizer prevents drastic changes in the pre-trained parameters of the model. These two proposed terms capture the persistent trade-offs that exist between the quantity of unlearning required and maintaining initial generation quality. Overall, our contributions are summarized as follows:
One of our key contributions is proposing a variational inference framework for unlearning in diffusion models. Specifically, we formulate the unlearning objective as variational divergence minimization and achieve class and feature unlearning in diffusion models.
To address the limitations of concurrent unlearning methods (Heng & Soh 2023 Fan et al. 2024 for diffusion models, which stem from assuming full access to the training datasct, our proposed method is more data-efficient. It is effective with fewer samples, requiring access only to the unlearning data points, and making it highly suitable for stricter unlearning scenarios with limited access to the original training dataset.
We propose a methodology to unlearn different classes from a pre-trained unconditional Denoising Diffusion Probabilistic Model (DDPM) (Ho al. 2020) trained on MNIST (LeCun et al. 1998). CIFAR-10 (Krizhevsky et al. 2009). and tinylmageNet (Le & Yang. 2015) datasets. We further validate our method for unlearning the generation of particular indetiidett features from a pre- trained Stable Diffusion Model (Rombach et al.] 2022) trained on the LAION-5B datasct (Schuhmann
et al. 2022
2 Related Works
2.1
Machine Unlearning for Generative Models
The core of machine unlearning (Cao & Yang 2015 Xu et al.
2020 Nguyen et al. 2022 Bourtoule et al., revolves around removing forgetting specific subset of training data from trained model. A
2021
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plausible approach is to retrain the model on the training data devoid of the undesired training data subset. However, this can be computationally very expensive concerning the scale of the model parameters and training data, To solve this problem, different machine unlearning algorithms were proposed for different problems and model settings, such as for K-means (Ginart et al. 2019). random forests (Brophy & Lowd 20210, linear classification models (Guo et al. 2019 Golatkar el al., 2020a b; Sekhari el al. 2021). neural
network-based classifiers (Wu et al. 2020 Graves ct al., 2021 Chundawat, et al., 2023a Panda et al. 2024).
Further, machine unlearning is also useful for generative settings. With the emergence of large pre-trained
text-to-image models (Rombach et al.) 2022 Saharia et al., 2022), there is potential for misuse in generating
harmful or inappropriate content. Thus, controlling the outputs from these generative models becomes an utmost priority. To solve this problem, recent works (Sun et al. 2023 Tiwary et al.) 2023 Moon et al, 2024) proposed unlea unlearning- ceraannng-based approaches for variational auto-encoders (VAEs) and generalive adversarial networks (GANs). Sun et al. (2023) proposed a cascaded unlearning method using the idea of latent space substitution for a pro-trained StyleGAN under both scttings of full and partial access (similar to our sctting) to the training astaset. To extend unlearning for diffussin models, a recent work (Heng & Soh 2023) adopts continual learning setup and proposes an unlearning method based on elastic weight consolidation (EWC) KKrkkatricck et al.) 20177] for unlearning pre- traiedd conditional DDPM (Ho et al. 2020). Further to enhance the performance of machine unlearning methods Fan et al. (2024) propose 'weight saliency' method inspired by input saliency. This method focuses on certain influential weights to unlearn both in classification and generative models.
2.2 Variational Inference
To acquire exact inference from data, it is essential to calculate the exact posterior distribution. However, the exact posterior is often intractable and hard to calculate essentially making the inference task challenging. To solve this problem, the domain of variational inference tries to approximate the true posterior by a more tractable distribution from class of distributions. Now to get the optimal distribution, often termed as variational posterior, these methods (Sato) 2001 Broderick et al.) 2013 Blundell el. al. 2015 Bui al.] 2016) optimize the so-called evidence lower bound (ELBO). These methodologies formulate the problem of inference in the parameter or weight space, which is often challenging because of the high dimension of the parameter space and multi-modality of parameter posterior distribution. Thus, to solve this problem,
the recent line of works (Ma et al., 2019: Sun et al.) 2019 Rudner et al.) 2020 Wild et al. 2022 try to do inference in the function space itself. These methods (Rudner et al. 2020 Wild et al. 2022) perform inference by optimizing functional KL-divergence, minimizing the Wasserstein distance between the functional prior and the Gaussian process. Inspired by these works, we formulate our unlearning methodology from task of inference in parameter space by minimizing a variational divergence.
3 Preliminaries
3.1 Unlearning Setup
Consider a pre-trained DDPM model, denoted as for, with initial parameters 0* E E C Rd. θ denotes the complete parameter space. This model has been trained on a specific training dataset D, consisting of m i.i.d. samples {- that are drawn from a distribution Px over the data space X, tries to learn the underlying data distribution Px. Based on the outputs of this model, the user wants to unlearn a portion of the data space consisting of undesired features, referred as Xy. Therefore, the entire data space can be expressed the union of X, and Xy, where X' Xx UX, X, = X',,, We denote the distributions over Xy and X, Px, and Px., respectively. The objective of the unlearning mechanism is to output sanitized model 6" that does not produce outputs within the domain Ny. This implics that the model should be trained to generate data samples conforming to the distribution Px, only. Assuming access to the whole training dataset, a computationally expensive approach to achieving this is by retraining the entire model from scratch using a dataset D, = {a Pt, or cquivalently, D, D \ Dy, where D, (nx) Px It is important note that we do not have access to D, in our setting. Hence, the method of retraining becomes infeasible. Figure 2 illustrates our proposed approach.
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Initial Model
Stability Regularizer
(0, 23)
2x 22
1-1
Unlearning Samples
D
8"
C0, D
Unlearned Model
Users
Model to be Unlearmed
a;)
(1
7)
||co
ca co !]
ar x:-1)
Plasticity Inducer
Figure Variational Diffusion Unlearning (VDU): Given user-identified samples be unlearned (Dy), the proposed VDU finetunes the initial model based on two-term loss function. The first term, the Plasticity Inducer (shown in the bottom half), minimizes the log-likelihood for the unlearned samples to eliminate their influence, while the second term, the Stability Regularizer (shown in the upper half), preserves the model's overall performance on the remaining data.
3.2 Background on Diffusion Models
In diffusion models, data generation formulated as a two-stage stochastic process. First, a forward diffusion process progressively corrupts clean data by adding noise according to Markov kernel q(-), resulting in sequence of latent variables that increasingly resemble pure noise. This forward process is fixed and fully specified by a predefined noise schedule. Second, a reverse (denoising) process reconstructs data by iteratively removing noise using a learnable Markov kernel p(.), which is typically parameterized by neural network. Learning in diffusion models, therefore, amounts to approximating the reverse process so as to invert the fixed forward diffusson dynamics. Let {x: / 0, 0,l,...,, T} denote latent variables with an denoting the true data. It is important mention that in the diffusion process, it is assumed that all transitional kernels are first-order Markov. Now, in the forward diffusion process, the transition kernel is denoted g( (x)-1) with the joint posterior distribution being ((21:1 (zn) I [( where cach g( (x.-.) . N(xi; /arat-1, (1 o.) Here, {ax, / E T} refers to the dilfussio model's noise scheduler where a; -T==10 aj. Similarly, for the backward diffusion process, the transitional kernel is denoted p(.,-1/æ;) with joint distribution p( p(=T) 11 (=( where, p(ær) (,7;; 7). Thus, after optimizing the diffusion model, the sampling procedure is done by sampling Gaussian noise from p(zr) and iteratively running the denoising transitions po(a;-1124 for T steps to generate new sample vo- eo is the true added noise, cœ( t) is the model predicted noise at time t.
4 Unlearning as Variational Divergence Minimization
Given the pre-trained DDPM model fe- and unlearning data subset D,, the objective is to produce an unlearned model d so that it behaves like a retrained model f" trained on D,.. Inspired by some previous works in Bayesian inference (ato 2001 Broderick et al. 2013 Blundell et al. 2015 Ghahramani Attias 2020 Nguyen et al., 2020),, it can be seen that, retrained parameters 6" are sample from the retrained model's 's parameter posterior distribution P()) i.e., Or P(O)),). Similarly, the pre-trained model's parameters 0* P(O) D,, Dạ). Using this motivation, try to approximate the retrained model's parameter posterior distribution P(O D.) as follows: D,) x P())D..D;)
P(Dy(0) This true by applying Bayes' rule (ignoring the normalizing constant) and simple consequence of i.i.d assumption of data in D, and Dy-
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It can be seen that the posterior distribution P,) is intractable, and approximation is required by forming proj(
& (0). Here, proj(-) is projection function that takes an intractable unnormalized distribution and maps it to a normalized distribution. As previously mentioned in the literature (Broderick
ctt al. 2013 Blundell et al. 2015 Bui et al.) 2016 Nguyen et al.) 2018 Noel Loo 2021: Knoblauch et al.
2022 Wild et al. 2022,, one can lake several choices projection functions, such as Laplace's 's approximation,
variational veereeeeeeece minimisation, moment matching, and importance sampling. Here, we consider the variational KL-divergence minimization for our method because previous works (Bui et al. 2016) noted that it outperforms other inference techniques for complex models. Thus, method is defined through variational KT.-divergence minimization over set of probable approxinate posterior distributions Q as follows:
P( P(Dyl0)
(7) = argminDxL ((()) Q(1)EQ
(1)
Here Z is the intractable normalization constant, which is independent of the parameter 0. Finally, taking the Gaussian mean-field assumption in the parameter space i.e. if the variational posterior distribution - No, of) and the posterior distribution with full data P(0) Dr, Dy) I (((,,,7) Eq.
reduces to minimizing the following loss function for a diffusion model. We refer this loss as the Variational Diffusion Unlearning (VDU) loss, which is defined as follows.
-1-08 az) ar(1 ā,-1) ||50 eelvana + vI ayeo, 1)
(0,
LvDu(0,0", - -
E
+7
zg Dy cg.!
20,²
:=1
B
Here y hyper-parameter, d is the model dimension. Eq. represents the proposed loss function used to optimize the pre-trained model during unlearning. The loss comprises two key terms: A is referred to as the plasticity inducer, and minimizes the log- likellidd the unlearning data. In contrast, the term B, serving as the stability regularizer, penalizes the model's parameters to prevent them from deviating too much from their pre-trained state during unlearning. To balance these two components, introduce hyper-parameter y. Figure detailed illustration of our framework and delails the different.
Variational Diffusion Unlearning
Input: Dj, 0* E, ?) ? Initialize: 0 2 0*
1: for t= = 1 to E do
2: Compute Lv 8" (
3: Update +- 0 - 1) dLvDU
end for
Output: FF
loss components used for the unlearning of Dy. Further, the estimation of μ and of is discussed in Appendix A.3.2
4.1 Theoretical Explanation for the Unlearning Loss
In this section, we provide a thcoretical exposition for the derivation of the variational diffusion unlcarning loss (0, DD) in Eq, from variational divergence minimization defined in Eq. [ This derivation is essentially presented as key theorem in Theorem [ The proof of this theorem essentially relies on the variational perspective of diffusion models, which is stated using Lemma and Lemma 2
Lemma 1 The log- likeliktdood under the backward diffusion process kernel,
In Inpo(1o) 2 Σ [Kr mn)
(x (po
(3)
Lemma 2 Assuming all the transition kernels to be Gaussian, the following hold:
1 - Cke
g(1,1122,, Fo) )= = (( (t)1 with (t
Va, It
(4)
v Tze /ay

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Published in Transactions on Machine Learning Research (03/2026)
po(14-110)) = No (000-11:0000) with po(t) = Vou
2t - vI di
at
(0(
(5)
(0) (tt)(1 ai-1) (1 σ4))
(6)
Proof for the above two lemmass (with different notations) be found in the existing literature (Shhl
Dickstein et al. 2015 Ho et al. 2020 Luo 2022 For completeness, we provide the proofs in Appendix A.1.1
and A.1.2
Theorem Assuming Gaussian mean-field approcimation in the parameter space i.e,, if the variational and the posterior distribution with full data Pr Dj)
posterior distribution Q(0) =
WEe, then
DRL (1(0) Z P(01D,,D.) P(D,10)
(1 at) ac Ō(-1)
2
Σ
E
||c0 - c0( f)|??
a ma)
Ey
t=2
(0
14)
o
+
+ log
(7)
20
20
0;
II
Proof 1 Here, we give rough sketch of the proof. The KL-divergence term in Eg. is expanded and segregated into two terms:
DeL (210) z. P(OID),
In Q(0)P(D,10)
E
(8)
1))
Q(1)
Z. p.
(g)
In Q())
[n [1)+
E
(9)
Q(9)
Q19)
D D,)
In Q(6)
In P(ro0))))))
EE
(10)
Q(6)
Q(0)
P(O)D,,D))
DoEDs
E (~)
Σ In P(mo moED,
(K::((0))P(0)))) D.))
(11)
(g) holds as the normalization constant independent of 0. (h) true because of the i.i.d. assumption on the data. We further derive the term @ E\>,, In P(raa(0) using Lemmas 1 and 2 While the second term
b = D distributions. For detailed proof, please look into Appendic 1A.133.
expanded using the assumption of KL divergence between two Gaussion
Remark 1 From Theorem the first term is further adapted and used in the first part of the loss function (0, 0r, D2) in Eq. ? Similarly, the second term II is further simplified with additional assumptions to obtain the second part of the loss. These details are included Appendia A.1.4
5 Experiments and Results
5.1 Datasets and Models
The primary goal of our proposed unlearning method is unlearn both class-level information and feature- level information. For class unlearning, our goal is to restrict. the generation of samples from certain

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Published in Transactions on Machine Learning Research (03/2026)
class. For this, we utilize unconditional DDPM (Ho et al.; 2020) pre-trained on three well-known datasets:
MNIST (LeCun et al. 1998), CIFAR-10 (Krishevsky et. al. 2009). and tinyInageNet (Le & Yang) 2015
Now for feature unlearning, we unlearn the generation of certain high-level features from a Stable Diffusion
model Rombach et al. 2022) pre-trained on the LAION-5B dataset (Schuhmann et al. 2022 about the model architectures and datasels can befound A Appendix
More details
A.4.1 A..en
5.2 Pre- Treanriinn Unlearning and Baselines
For class-unlearinng setting, in order achiove the pro-trained model, we train the unconditional DDPM model MNIST, CIFAR-10, and LinylmageNet (UIN) datasets. These pre-trained models achieve FID (Heusel et al.) 2017) scores of 5.12 on MNIST, 7.96 on CIFAR-10, and 18.92 on tinylmageNet datasets. For the Ceaturo-unlearning sctting, we use pre-trained checkpoints of Stable Diffusion model from an open-sourced repository. A detailed description of the pre-training setup can be found in Appendix A.4.2
Pro- Pro-Trainin::
Due to the unavailabilityy of the total training dataset, our experimental setting is restricted to partial access, ie., only to the data points belonging the unlearning class. For class- unlearnne,,,, we unlearn multiple classes from MNTST, CIFAR-10, and tinyImageNet datasets. Now, for feature-unleaninng, we try to unlearn some high-level features, such as an artistic style from a state-of-the-art Stable Diffusion model. Further experimental details of our unlearning method on each dataset and model are added in Appendix A.4.3
Unlearning Setup:
Baselines: If we assume that we have access to Dr then retraining is the most optimal method. Due to its high compulational cost, we fine-tune the model assuming access to D,. Each initial model is fine-tuned with D, for single epoch since it serves an optimal baseline when comparing various approaches. Further, we compare our proposed method against several unlearning baselines tested for diffusion models: Selective Amnesia (SA) (Heng & Sohi, 2023), Saliency Unlearning (SalUn) (aan et al., 2024), and Erasing Stable Diffusion (ESD) [Gandikota et al. 2023a)). Note that for a fair comparison, the loss component regarding D, is removed from all the above methods as we don't have access to D,.. Additionally, to account for the low computational cost of unlcarning methods, the unlcarning step for cach method is only executed for very few epochs (10x of fine-tuning time), and the best outcomes among these few epochs are reported for each method. The reason for putting such strict constraints is discussed in detail in Appendix A.3.4
5.3 Evaluation Metrics
Percentage of Unlearning (PUL): Proposed by Tiwary el al. (2023) this metric measures how much unlearning has occurred by comparing the reduction in the number of unwanted samples produced by the model after unlcarning (8t) with the number of such samples before unlcarning (0*). The Percentage of x 100% where (D9))- and (D))o- represent the number of undesired samples generated by the original and the unlcarned model, respectively. To calculato PUL, we generate 5,000 random samples from the unconditional DDPM model and use pre-trained classifier to identify the unwanted samples. Details of this classifier are given in the Appendix A.4.4
Unlearning (PUL) is calculated as: PUL = (D)))=-(D))o- (D)))-
To quantify the quality of generated images by the unlearned model, we utilize the u-FID score. It is important to mention that this FID score is measured between the generated samples from the unlearned model and D,.. Thus, in the case of unconditional DDPM, remove the unlcarning data points from the non-unlcarning data, we again use the same pre-trained classifier. In this case, a lower u-FID score reflecting higher image quality indicates that the unlearned model's performance does not degrade the non-unlearning data points.
Unlearned Fréchet Inception Distance (u-FID):
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5.4 Experimental Results
5.4.1
Quantitative and Qualitative Results
In Table [ we contrast our method, VDU, against the above- mentiondd baseline methods for different class unlearning settings. Overall, for all datasets and unlearned classes, it is observable that our method achieves lower u-FID scores with comparable to or superior PUL scores. Specifically, the MNIST dataset, VDU
Table 1: PUL(T) and (VF scores (mean over three random seeds) comparisons between VDU and different unlearning baselines for class unlearning on the MNIST, CIFAR-10, and tiny ImnymaeeNNe (UIN) datasets.
Fine-tuning
SalUn
ESD
VDU (Ours)
Datasets
Unlearned Classes
PUT (%)
u-FID
PUL (%)
u-FID
PUT (%)
u-FID
PUT (%)
u-FID
PUL (%)
u-FII
Digi-1
90.07
5.90
15.01
301.26
45.28
08.75
56.06
66.15
75.06
14.43
MNIST
Digit-8
91.29
6.15
48.95
161.09
32.53
50.18
32,68
55.67
68.96
38.20
CIFAR-10
Automobile
88.01
9.02
2.25
92.89
12.01
06.17
8.97
73.18
60.87
30.86
Ship
92.80
10.74
85.02
249.89
55.13
75.48
58.27
77.12
71.63
24.46
t1
Fish
82.56 32.56
13.75
67.7
32.00
39.33
42.70
41.67
45.19
58.75
29.92
Butcher Shop
83.37
16.82
6.7
24.00
2.87
33.47
8.76
39.48
66.67
24.17
MNIST (Unconditional DDPM)
CIFAR-10 (Unconditional DDPM)
(a) Original
(b) Unlearned
(c) Original
(d) Unlearned
(e) Original
(1) Unlearned
(g) Original
(h) Unlearned
Digst '1"
Digit
Digit '8'
Digit "8'
'Automobile'
"Automobile"
'Shäp"
'Sháp'
5
9
6
8
8
8
9 9
4
7
6
8
8
8
/
5
/
/
8
4
2
8
8
8
(
6 9
SinyIageNee (Unconditional DDPM)
LAION-5B (Stable Diffusion)
(8) Original
()) Unlearned
(k) Original
(1) Unlearned
(m) Original
(a) Unlearned
(o) Original
(p) Unlearned
'Goldfish'
Goldfish
Butcher Shop Butcher Shop
Busy Street'
Van Vang-Gogh style"
'Car near tunnel!
'Car object'
Figure 3: Generated samples from the pre-trained model and different unlearned models. (d) & (1) are generated using the same noise vectors from unlearned unconditional DDPM on MNIST, CIFAR-10, and tiny ImageNet datasets. (m)-(p) show Stable Diffusion samples before and after unlearning the VVn Gogh style' and 'Car object' using prompts from LAION-5B. More results provided in Figure and Figure in Appendix.
outperforms all other baseline methods, with large improvements in u-FID, after just epoch of training. Similarly, for LinylmageNet, VDU achieves high PUL scores for unlearning "Butcher Shop' compared to all other baseline methods. To summarize, it can be seen that method retains superior to comparable PUL with superior u-FID scores across variety of class unlcarning scenarios over multiple datasets. Similarly, the performance of VDU for unlearning features from a pre-trained Stable Diffusion model is shown in Figure 3. This shows that VDU is applicable not only for low-dimensional settings but also works well in nigh-dimensional datasets trained on state-of-the-art Stable Diffusion models. More experimental results can be found Appendix A.2
5.4.2 Ablation Results
Effect of Unlearning Epochs: Table reports the performance of our method across different unlearning epochs. We observe that inereasing the number of unlcarning epochs improves the degree of unlearning, while simultancously degrading the generation quality. This behavior can be intuitively explained by our objective function: the first term of the loss is unbounded, and continued minimization increasingly suppresses the
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Table 2: Effect of training epochs on unlearning performance measured on VDU
Epoch
Epach 2
Epoch 3
Epoch 4
Epoch 5
Dataset
Unkearned Class
PUL (%)
u-FID
PUL (%))
u-FID
PUL (%)
u-FID
PUL (%)
u-FID
PUL (56
u-FID
MNIST
Digit-1
86.58
106.18
100.00
CIFAR-10
Automobile
27.33
26.82
43.67
30.19
50.58
29.82
60.87
30.86
68.97
56.82
dayluaggeet
Fish
33.26
18.72
58.75
29.92
59.86
37.68
39.88
52.72
60.65
70.95
Unlearning Concept "Van_ Gogh"
Prompt "a fiery sunset over rolling fields in the style of van gagh
Orignd
Uniearmed epoch=]
Unlasmmd epoch-2
Unleammed epcch:
Unieamed epoch-4
Unlearmed esoch::5
Unlearning Concept "Car*
Prompt "e car going
Original
spachel
spoch-2
spach=3
spachee
epeched
spache8
epach-)
spacheil
epech-g
spach-10
Figure 4: Results of VDU on unlearning VVan Gogh style' and *Cur object' over multiple epochs
largeted features, thereby enhancing unlearning. However, this aggressive optimization drives the model further away from the original model in parameter space, leading to deterioration in generation quality. Figure 4 visually highlights this inherent trade-off between unlearning effectiveness and generative fidelity. For these experiments, we set the gamma to be 0.3 for all the datasets. We see a similar trend in the visual results of Figure Figure and Figure 10 for feature unlearning in Stable Diffusion.
Contribution of y: We evaluate the reliance of our method on the hyper- prper-parameter Y [0, 1]. In Table MNIST (unlearning the digit "1'), CIFAR-10 (unlearning "Ship" )
illustrate the impacts of varying and tinyTmageNet. (unlearning "Butcher Shop"). Tt can be seen that, with increasing Eq. tends towards increasing the strength of the stability regularizer. This leads to the the model degenerating into the pre-
MNIST
CIFAR R-1R--10 10 (Ship)
(Digit "1')
100
100
U-FID and PUL(%)
U-FID and PUL((%)
80
80
Table 3: Impact of the unlearning per- formance of VDU.
60
60
40
40
MINIST (Digi-1) CIPAR-10
(Butcher
20
20
14:33
28.75
20.51
55.65
0.1
0.3 0.5 0.7
0.1 0.3 0.5 0.7
0.5
71.67
13.12
60.35
19.64
68.86
20.52
16.84
7.48
1.67
13.16
20.56
21.08
y
Figure 5: Ablation results on varying y for class unlearning of MNIST and CIFAR-10 datasets. Increasing value of 7 results in decrease in PUL and u-FID metrics.
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trained model. Due to this, observe steady decline in PUL since the proposed loss attends to preserving the generated sample quality only. Such a trend is also bolstered by the lowering of the u-FID, indicating good sample quality. A visual representation of these trends is depicted in Figure
MNIST Unlearn Digit '1'
CIFAR-10 Unlearn 'Ship' Y=
7=0
7 =
1
==
26
6
4
3
5
0
6
7
8
5 2
9 3
/
5 2
550 4
9 4
g 6
2 27033
7
8
5 1 13330
1
8
4
4 7 7
6
6 8 0
3
2
7
3
Figure 6: Visual illustrations of generated image samples with y and 7 on MNIST and CIFAR-10 for the class unlearning setting.
Nullify Loss Components: Nullifying loss components with y= and 7=1 for unlearning Digit-1 in MNIST and Ship class in CLFAR-10 are shown visually in Figure 6 We observe that when 7=0 or when the stability regularizer is nullified, the quality of generated samples drastically declines and images of the Digit-1 and Ship classes are not generated. On the other hand, image quality increases when 7=1, 1, but class-specific information is still preserved, leading to the generation of Digit-1 and Ship classes. Overall, by varying Y, our proposed loss strives to achieve a balance between unlcarning and preserving image quality.
6 Conclusion, Limitations and Future works
In this paper, we present Variational Diffusion Unlearning (VDU), a machine unlearning framework prevent the generation of undesired outputs from pre-trained diffusion model, with sole access the training data subset to be unlearned. Our current theoretical framework leverages the parameter space to exploit variational inference by minimizing loss function comprising two key components: the plasticity inducer and the slabilily regularizer. While the plosticity inducer focuses on minimizing the log-likelihood of the undesired training samples, the stability regularizer preserves the quality of the generated image samples by regularizing the model in the paramcter space. Through comprehensive experiments, we demonstrate our method's effectiveness in different class unlearning settings for the MNIST, CIFAR-10, and tiny Tmageeagee dat asets. Further, the effectiveness of our approach is bolstered by various feature unlcarning from statc-of-the-art Stable Diffusion models pre-trained on LAION-5B dataset. This highlights that under restricted access to the training dataset, our method is effective for both low and nigh-dimensiooal settings, making it practical choice unlearning from diffusion models.
Apart from its effectiveness, we highlight some key limitations, such as our current framework assumes a Gaussian mean-field approximation on the parameter distributions that might not always be valid. Thus, exploration of more generic distributional settings left as a part of our future work. Also, additional empirical evaluation as per the recent unlcarning benchmarking datasct (Zhang et al., 2024) is key limitation and left as part of future work. Further to overcome the limited theoretical scope of variational inference in parameter space, broader theoretical framework using function space variational
Limitations and Future works:
inference techniques Ma et al. 2019 Rudner et al. 2020: Sun et al. 2019
Wild et al. 2022). will also be
explored in our future work.
Acknowledgments
Subhodip, a current Ph.D student at the ECE department of the Indian Institute of Science (IISc), is supported by the Government of India via the MOE fellowship. Prathosh would like to acknowledge the support provided by the Indian Institute of Science and Infosys Foundation for setting up the compute infrastructure with generous startup grant.
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References
Ho Bae, Jachee Jang, Dahuin Jung, Hyemi Jang, Heonseok Ha, Hyungyu Lee, and Sungroh Yoon. Security and privacy issues in deep learning, ar preprint arX 11655, 2018.
Charles Blundell, Julien Cornebise, Koray Kavukeuoglu, and Daan Wierstra. Weight uncertainty in neural network. In International Conference on Machine Learning, 2015.
Lucas Bourtoule, Varum Chandrasekaran, Christopher A Choquette- Choo, Hengrui Jia, Adelin Travers, Baiwu Zhang, David Lic, and Nicolas Papernot. Machine unlearning. In 2021 IEEE Symposium on Security and Privacy (SP), pp. 141-159. IEEE, 2021.
Tamara Broderick, Nicholas Boyd, Andre Wibisono, Ashia C. Wilson, and Michael I. Jordan. Streaming variational bayes. In Proc. of NewrIPS, 2013.
Jonathan Brophy and Daniel Lowd. Machine unlearning for random forests. In International Conference Machine Learning, pp. 1092-11044 PMLR, 2021.
Thang Bui, Daniel Hern andez=Lobato, Jose Hernandez-Lobato, Yingzhen Li, and Richard Turner. Deep gaussian processes for regression using approximate expectation propagation. In International Conference on Machine Learning, 2016.
Yinzhi Cao and Junfeng Yang. Towards making systems lorget with machine unlearning. In 2015 IEEE symposium on security and privacy, pp. 463 480. IEEE, 2015.
Duygu Ceylan, Chun-Hao P. Huang, and Niloy J. Mitra. Pix2video: Video editing using image diffusion. In Proc. of TCCV, 2023.
Vikram S Chundawat, Ayush K Tarun, Murari Mandal, and Mohan Kankanhalli. Can bad teaching induce forgetting? unlearning in deep networks using incompetent teacher. In Proc. of AAAT, 2023a.
Vikram S. Chundawat, Ayush K. Tarum, Murari Mandal, and Mohan Kankanhall.. Zero-shot machine unlearning. IEEE Transaction of Information Forensics and Security, 2023b.
Chongyu Fan, Jiancheng Liu, Yihua Zhang, Eric Wong, Dennis Wei, and Sijia Liu. Salun: Empowering machine unlearning via gradient-base weight saliency in both image classification and generation. In Proc. of ICLR, 2024.
Ruoyu Feng, Wenming Weng, Yanhui Wang, Yuhui Yuan, Jianmin Bao, Chong Luo, Zhibo Chen, and Baining Guo. Ccedit: Creative and controllable video editing via diffusion models. In Proc. of CVPR, 2024.
Rohit Gandikota, Joanna Materzynska, Jaden Fiotto-Kaufman, and David Bau. Erasing concepts from diffusion models. In Proc. of ICCV, 2023a.
Rohit Gandikota, Joanna Materzynska, Jaden Fiotto-Kaufman, and David Baul. Erasing concepts from diffusion models. In Proc. of ICCV, 2023b.
Zoubin Ghahramani and H. Attias. Online variational bayesian learning. Workshop on Online Learning, NewrIPS, 2020.
Antonio Ginart, Melody Guan, Gregory Valiant, and James Zou. Making ai forget you: Data deletion in machine learning. Advances in neural information processing systems, 32, 2019.
Aditya Golatkar, Alessandro Achille, and Stefano Soatto. Eternal sunshine of the spotless net: Selective forgetting in deep networks. In Proc. of CVPR, 2020a.
Aditya Golatkar, Alessandro Achille, and Stefano Soatto. Forgetting outside the box: Scrubbing deep networks of information accessible from input-output observations. In Proc. of ECCV, 2020b.
Ian Goodfellow, Jean Pouget-Abadic, Mchdi Mirza, Bing Xu, David Warde-Farlcy, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial networks. Communications of the ACM, 63(11): 139-144, 2020.
12

---

Published in Transactions on Machine Learning Research (03/2026)
lan J. Goodfellow, Mehdi Mirza, Da Xiao, Aaron Courville, and Yoshua Bengio. An empirical investigation of catastrophic lorgetting in gradient-based neural network. In Proc. of International Conference on Learning Representations, 2014.
Laura Graves, Vineel Nagisetty, and Vijay Ganesh. Amnesiac machine learning. In Proc. of AAAT, 2021.
Chuan Guo, Tom Goldstein, Awni Hannun, and Laurens Van Der Maaten. Certified data removal from machine learning models. arXiv preprint arXiv:1911. 030000, 2019.
Alvin Heng and Harold Soh. Selective amnesia: A continual learning approach to forgetting in deep generative models. In Proc. of Newral Information Processing Systems, 2023.
Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by two time-scale update rule converge to local nash equilibrium. Advances in neural information processing systems, 30, 2017.
Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. In Proc. of NeuRIPS, 2020.
Diederik P Kingma. Auto-encoding variational bayes. arXiv preprinl Xrx:::3322.6111 2013.
James Kirkpatrick, Razvan Pascanu, Neil Rabinowitz, Joel Veness, Guillaume Desjardins, Andrei A Rusu, Kieran Milan, John Quan, Tiago Ramalho, Agnieszka Ctrassaa-Barwinge et al. Overcoming catastrophic forgetting in neural networks. Proceedings of the national academy of sciences, 114(13):352133526, 2017.
Jeremias Knoblauch, Jack Jewson, and Thcodoros Damoulas. An optimization-ccntric view on bayes' rule: Reviewing and generalizing variational inference. In Proc. of Journal of Machine Learning Research, 2022.
Alex Krizhovsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. University of Toronto, 2009.
Ya Le and Xuan Yang. Tiny imagenet visual recognition challenge. pre-prind Semantic scholar, 2015.
Yann LeCun, Lóon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient- lcarning applicd to document recognition. Proceedings of the IEEE, 86(11):2278 22,22224, 1998.
Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaoou Tang. Deep learning face attributes in the wild. In Proceedings of International Conference on Computer Vision (ICCV), 2015.
Calvin Luo. Understanding diffusion models: A unified perspective. arXiv pre-print, 2022.
C. Ma, Y. Li, and M. Hernándezz-Loatto Variational implicit processes. In International Conference on Mochine Learning, PMLR pages 4222- 2222,,23,,11 2019.
Michael McCloskey and Neal J. Cohen. Catastrophic interference in connectionist networks: The sequential learning problem. Psychology of Learning and Motivation, 1989.
Saemi Moon, Seunghyuk Cho, and Dongwoo Kim. Feature unlearning for pre-trained gans and vaes. arXiv preprint, 2024.
Cuong V. Nguyen, Yingzhen Li, Thang D. Bui, and Richard E. Turner. Variational continual learning. In Proc. of ICLR, 2018
Quoc Phong Nguyen, Bryan Kian Hsiang Low, and Patrick Jaillet. Variational bayesian unlearning. Advances in Neural Information Processing Systems, 33:16025-1603, 2020.
Thanh Tam Nguyen, Thanh Trung Huynh, Phi Le Nguyen, Alan Wee- Chung Liew, Hongzhi Yin, and Quoe Viet Hung Nguyen. A survey of machine unlearning. arXiv preprint arXiv:2209.0222 2022.
Alexander Quinn Nichol and Prafulla Dhariwal. Improved denoising diffusion probabilistic models. In International conference on machine learning, pp.
PMLR, 2021.
13

---

Published in Transactions on Machine Learning Research (03/2026)
Richard E. Turner Nocl Loo, Siddharth Swaroop. Generalized variational continual learning. In Proc. of ICLRR 2021.
Subhodip Panda and Prathosh A.P. Fast: Feature aware similarity thresholding for weak unlearning in black-box generative models. arXiv pre-print, 2023.
Subhodip Panda, Shashwat Sourav, and Prathosh A.P. Partially blinded unlcarning: Class unlcarning for deep networks a bayesian perspective. arviv pre-prinl, 2024.
Adilya Ramesh, Mikhail Pavlov, Gabriel Goh, Scott Gray, Chelsea Voss, Alec Radford, Mark Chen, and Πly Sutskever. Zero-shot text-to-image generation. In International Conference on Machine Learning, pp- 8821 8831. PMLR, 2021.
Aditya Ramesh, Prafulla Dhariwal, Alex Nichol, Casey Chu, and Mark Chen. Hierarchical text-conditional image generation with clip latents. arXiv preprint arXiv:2204.061 1(2):3, 2022.
Robin Rombach, Andreas Blattmann, Dominík Lorenz, Patrick Esser, and Björn Ommer. High-resolution
image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 10684-10695, 2022.
Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. In Medical image computing and computer-asee assisted CitrruntiionMMICCAA 2015: 18th international conference, Munich, Germany, October 5-9, 2015, proceedings, part III 18, pp. 234-241. Springer, 2015.
T. G. Rudner, Z. Chen, and Y. Gal. Rethinking function-space variational inference in bayesian neural networks. In Third Symposium on Advances in Approzimale Buyesian Inference, 2020.
Levent Sagun, Utku Evci, V Ugur Guney, Yann Dauphin, and Leon Bottou. Empirical analysis of the hessian oveo-vorrttt wver-parametrized neural networks. arXiv preprint arXiv:1706.04 2017.
Chitwan Saharia, William Chan, Saurabh Saxena, Lala Li, Jay Whang, Emily L. Denton, Kamyar Ghasemipour, Raphael Gontijo Lopes, Bureu Karagol Ayan, Tim Salimans, et al. Photorealistic text-to-image diffuusion models with deep language understanding. Advances in neural information processing systems, 35:36479- 36494, 2022.
Masa-Aki Sato. Online model selection based on the variational bayes. In Proc. of Neural Computations, 2001.
Patrick Schramowski, Manuel Brack, Björn Deiscroth, and Kristian Kersting, Safe latent diffusion: Mitigating inappropriate degeneration in diffusion models. In Proceedings of the IEEE/CVF Conference on Compuler Vision and Pattern Recognation, pp. 22522-22533 2023.
Christoph Schuhmann, Romain Beaumont, Richard Vencu, Cade Gordonand Ross Wightman, Mchdi Cherti, Theo Coombes, Aarush Katta, Clayton Mullis, Mitchell Wortsman, Patrick Schramowski, Srivatsa Kun- durthy, Katherine Crowson, Ludwig Schmidt, Robert Kaczmarezyk, and Jenia Jitsev. Laion-5b: An open large-scale dataset for training next generation image-text models. Conference on Neural Information Processing Systems (NeurIPS), 2022.
Ayush Sekhari, Jayadev Acharya, Gautam Kamath, and Ananda Theertha Suresh. Remember what you want to forget: Algorithms for machine unlearnings. In Proc. of NearIPS, 2021.
E. Weiss, N. Maheswaranathan, and S Ganguli. Deep unsupervised learning using nonequilib- rium thermodynamics. In International Conference on Machine Learning (ICML), pp. (2256-2265) pmlr, 2015.
Yan Song and Stefano Ermon. Generative modeling by estimating gradients of the data distribution. In Proc. of NeuRIPS, 2019.
14

---

Published in Transactions on Machine Learning Research (03/2026)
Yang Song, Jascha Sohl-Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. In Proc. of TCL.R, 2021.
Hui Sun, Tianqing Zhu, Wenhan Chang, and Wanlei Zhou. Generative adversarial networks unlearning. arwi preprint, 2023.
S. Sun, G. Zhang, J. Shi, and R. Grosse. Functional variational bayesian neural networks. arviv preprinl $tt::1990005770 2019.
Piyush Tiwary, Atri Guha, Subhodip Panda, and Prathosh A.P. Adapt then unlearn: Exploiting parameter space semantics for unlearning in generative adversarial networks. arXiv pre-print, 2023.
Tatiana Tommasi, Novi Patricia, Barbara Caputo, and Tinne Tuytelaars. Advances in Computer Vision and Pottern Recognition. Springer, 2017.
Veit David Wild, Robert Hu, and Dino Sejdinovic. Generalized variational inference in function spaces:
Gaussian measures meet bayesian deep learning. In proc. of Neural Information Sylems, 2022.
Yinjun Wu, Edgar Dobriban, and Susan Davidson. Deltagrad: Rapid retraining of machine learning models. In International Conference on Machine Learning, pp.
PMLR, 2020.
Heng Xu, Tianqing Zhu, Lefeng Zhang, Wanlei Zhou, and Philip S. Yu. Machine unlearning: A survey, ACM Computing Surveys Vol. 56, No. 1, 2020.
Yihua Zhang, Chongyu Fan, Yimeng Zhang, Yuguang Yao, Jinghan Jial, Jiancheng Liul, Gaoyuan Zhang, Gaowen Liu, Ramana Kompella, Xiaoming Liul, and Sijia Liul. Unlearncanvas: A stylized image dataset for enhanced machine unlcarning evaluation in diffusion models. Conference Newral Information Processing Systems (NeurIPS 2024) Track on Datasets and Benchmarks., 2024.
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A Technical Appendices and Supplementary Material
A.1 Theoretical Analysis
A.1.1 Proof of Lemma-1
Let To denote the true data. Thus, to increase the log-likelihood of the data, we maximize the evidence lower bound as follows:
In po In / po((o:T) dæi.
(12)
In /
po(Lu:))
( (o)) dæ
(13)
g (o))
Po (xo
In
(14)
of (mo)
1 ( (20))
(a)
In po (NO.T)
E
(15)
q(ar mo)
(x [mo)
p(2T) IT- Po (o (
F (())))
In
(16)
Il (1 (1)
pl ((T))pp (2oo (11) IT Po (2t (xt)
E
In
(17)
q(zurlaa (2))
((11 (xo) 1= (
(za [1 (
(b)
p(rr) (po x1 (=2 Pe (re-11 221)
E 0(Furlo
(18)
((21|20)
2 (2 r 12-1, 20)
Po (o
po (2t - (1re)
E ((s1))l
In ((11)10))
In
(19)
(1 T+ 1, F0
em
In ((Tr)po(ro((r) ((11)200)
po (xte (x2))
E ((ar)))))))
In
(20)
g(
lane .o (g (z0)
t=2
(110)
p (20 In ( (2ro) ((21(10))
T
po po (20)
E q(=u)(a))
In
In II
(21)
q(xx (mo)
g 1 Ire, xoo
t= (2ts)
In pl p(xT)po(Eoler ((IT(10)
T
(Ix po
Po
In
(22)
((x)))19))
g(Ie - 1 ID)
In p(xT)
T
po pa(x (2:)) In
E q( (x))
(o +
E
(23)
((
q( xo))
1=2 q (m))
q (11=1 [ee 200)
(d)
In p(xT)
In po /2:2)
E
E
E
(24)
g (2))
g( m0)
q( (ro)
1= q( lmo))
q( 1r 200
(e)
E
[In (xol - D
(25)
a (mr)
E Dea_lofa--lee,,mmllllooc-----
(26)
Σ
E (Pku(g(ee-1(e,, (m)l)o))
20)
(27)
Here (a) holds via Jensen's inequality as log is a concave function. (b) is true because additional conditioning doesn't. affect the first-order Markovian transitional kernel q(-1-)- (c) and (e) are achieved via Bayes' rule
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Published in Transactions on Machine Learning Research (03/2026)
while (d) is true via marginalization property. As the two terms in Eq. 25 are insignificant compared to the
term in Eq. 26 so (/) holds.
A.1.2 Proof of Lemma-2
Even though is a three-part proof, part-(3) comes from the proof of part-(1) while part-(2) is proved via a similar argument as the proof of part-(1). So, here we will prove part-(1) in detail. We know:
q(11/2=-1, = =0(2((2211) (x4s (1-
(28)
Now, we can represent 2, in terms of zu by recursive ro-paramcterization as,
2x Vajat-1 v1 014--1
(29)
Vai
Vai- + 11 a1-01-16-)) + vI -1-----
(30)
-V104-121--
0204-191-2 + vI - a,9-11
(31)
10:04-14--1 - (V (Va--000--1 (11 01) (2)221
(32)
/0:01-14--2 a: 0:04-11 0::6-2
(33)
V0.04-1 14--2 V
0104-116-2
(34)
(35)
04 +
II
0650
(36)
1=1
2g + vI 0gE0
(37)
Thus, It ~ N((z Varzo, (1 a)) Now, via Bayes' rule:
((1e-1/21,00)
(38)
g(
N( 20 (1 V0 -1- -d
(39)
(xz (artz-1)²
(xI-1 v a
(2, va
x exp
(40)
2(1 at))
2(1 - a1-1)
2(1 - ai.)
(xt Varte-1)2
(x1-1 Vai--111
(It )
exp
(41)
1 - --7-1
Cx
2 /aptttti11 + axpt
x/ - 2
exp
+
+ Clx,, 20)
(42)
2
1 1-
- Ō:-1
exp
1
-2 -2
Q-31-1
+
41-1
2
2/44-182-1270
(43)
1-at at
1 1-a-11
a:-1
1 a
1
Vaja's
V 100-1200
exp
x4-1
-2
Ft-1
(44)
a4
1
Ō4-1
C/
1 ū
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Published in Transactions on Machine Learning Research (03/2026)
Upon further expansion of Eq. 44
eep
ar(( ār 1) + 1 - Ott
2/--1 -2
2
Vanii
10
Ft 1
(45)
2 (1 - 0z) (1 Ō1-1)
1 Ct
1 04+ 0
exp
(1 at
a: - at + 1 - at
-r-1 1)
1/-1 2
2
at
1 Ct-1
/20-120
It-
(46)
1 1- α1
Vanta
100
exp
2 (1 04
a(-1) 1)
1- - 2
2
1- at
+
1 Ōt-1
1t-1
(47)
1 - α1
v var
+ va4-120
(1 - a.) (1 - -a
exp
2
04
01)(1
0t-1)
1 -2
1 1-0x 0t
04-1
1 āt
I2-1
(48)
- 02
Vai(1 -a--1) + vōr-1 02)
exp
2
04) (1
(4-1)
x/-1 2
1 āt
Te-11 1
(49)
Vail1 0x-1) )rr V va--1(1 ax)20
(1 - an)(1 اy-1)
x NN(
12-1;
(50)
1- dt.
aq
From Eq. 50 it can be seen that,
,t(()= (1- (1-a))(1 - 11-1) (1 ar)
(c(() Van(1 - Cz- ).c, + va- ax)
1 az
Now further substituting zo Te-yT-a en from Eq. 37 in the mean term (t(t), we get, vaz
(t(1) vor(1 5z Jose + vol- - 020)
(51)
at
Vor(1
5 )ost + v0t-1(1 - O1.)
21 -it0
Vol
(52)
1 --ai at
Var(1
αt 105t + (1 a1))
S4 Bt-y Ml-yT-orre
Voie
(53)
1- 02
Var(1
5(-1) ),1
(1- - a, 20
(1 1 0z) 11 1 a.e
(54)
1- az
(1 at) V at
(1 --aa) ar
Vai(1 - 1))
1 - at
(1aa)) at)/1 at
+
D1
Co
(55)
1 at
(1 ot)
(1 a+) Va
[1(( a1-1)
04
(1 an)vI I aa
(1 az) Vas
+
(1 - āa)
It
Vas
E0
(56)
ag ā +
at
(1 - az) /
(57)
(1 az) Vai
v 0
1 áz
(1 az) 1 02 60
(58)
āz) Va
Var
(1
D2
60
(59)
Vat
Var
Along the similar lines we can prove that, Ha(t)= = 1
Va."
xt-
(1
Vac
Ea (2),
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A.1.3 Proof of Theorem-1
The variational divergence term in Eq.
DKL [200) z.
P()
In Q(0)P(D,10)
(60)
1(D
Q())
7. p( Dr)
Q(0)
[n P(D, 10] 1 E
In
(61)
Q(0)
Q(0)
D, D,)
Q
Σ mi Eo
In P(ro00)
662)
Q
Q(0)
P( D.)
In P(x0
(KL(Q(0)[(()))) D,))
663)
(
FoEDD
(g) holds as the normalization constant is independent of f. (h) is true because of the ii.d. assumption on the data. We further derive the terms and 1 of Eq. 63 below.
Further derivation of term @:: For further simplification of this term, we would require some more theoretical formulations as follows:
Lemma 3 The Kullback-Leahh divergence for two mullivariate normal distributions is given by:
Eyg d tr(Ey'Ez) + (Hy - Mx) Ey (1g mox)
DKL(N(Z: Me, Ho, Eg))
log
Σzl
Proof 2 Proof of this lemma can be found in any standard information theory tertbook and is avoided here.
From Lemma 2 we know that q(x=-11 1 zo) = (X (t). og(+))) with (t(() Va 2t 1-ai
/1-āey/ai and
po( [2,) = (o (t) with (t()) = var Iz - /o (=),,)) where (t (1-a))
1-ar
(1-&c)
Now using this and the above Lemma 3 the KT-divergence in the ELBO term of Lemma 1 can be written follows:
L ( 20) (1
(64)
DeL (N (M Mg: 2ig(t) || (( (t)(
(65)
1
1 -
1
- 02
Va Dt
co(xett)=
+
(66)
(0?
VT- 0iyar
Va:
vI
1
1
- Cr.
1-
2
20²(1)
VI ai aiva
co /1-aiyay
co ao(xee
(67)
2
1
a4
(co c0( t))
(68)
(t)
VI 11-aaya alyay
(1-az)²
1|co - co( 1
(69)
20²(t)(1 ar)a
(1 (1))
||c0 co(st, 1)
(70)
(1 -
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The first term @ of Eq. 63
be expressed using Monte Carlo estimation follows:
Σ In P(zol0)
(71)
Q~Q
Po
M
Σ FoEDs
In P()
(72)
M
2
E [ (xt-1 [mxe))]
(73)
(xo)
moED,
T
an)
Σ
|Ico - co(2,,,)]l
(74)
ZoEDj 1=2 [0)
ar(l - a(-1)
holds a consequence of Lemma Now using crude estimate of M (i.e. denoting 01 we are minimizing with respect to the variable f) and equation 70 (5) holds.
Further Derivation of term D:
Using the above Lemma 3 with the variational posterior distribution
Q(0) = No, and the posterior distribution with full data Pro = - NWt,, this term can be simplified as follows:
In o. +
of + (0; - -14))
(=:(()))))))))) =
(75)
200²
Finally, incorporating both the terms @ and b terms Eq.
and Eq. 75
respectively we gel,
DKL (210) Z P(ODD,D.) D.)
(1 az)
2
Σ
E
1|co - co(x2, t)1
P(D,10)
EDED t=2 g(z{/20)
ar xx-1)
(0; 22)
o²
log 0¹¹
20
2
A.1.4 Loss function Derivation
Adaptation of part-7 in VDU: Note that the term of the lower bound above computationally expensive and memory intensive because for each xo Dy we need to add noise for all values of E (2...., T and then denoise again for each t. Now, if T is very large, this essentially increases the sample size OTT).
Thus, to avoid this, if we simply apply the idea from the previous work (Ho et al. 2020 this be written follows:
(1 (1-az)
-=
E t=2 {(x1220
|lco co(
(76)
[a((1 a(-1)
ZoED,
(1 - ar)
E
|1:0 e0l Solvãnoo + v1 - -isto 1)
(77)
(1 x4-1)
oo.t
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Adaptation of part-II in VDU: Assuming P,) is mean-shifted version of P(0)Dr, Dy) with the same variance factor L.e. with 0 of term IT turns out to be as follows:
d
(0; 1
of + log of 1
11
20 2
20
2
(0; u
1
+
+ log
20
2
2
==1
(0: 2
20
This simplified version is used the second component of our proposed loss function. The reason for assuming = of is to simplify the optimization process. However, one can remove this assumption and optimize with respect to 0; to find the optimal variance factor of P,))
A.2
Additional Results
A.2.1
Quantitative Results using VDU
Table 4 presents the unlearning performance of the VDU method across various classes from MNIST, CIFAR- 10, and Imageeet datasets for different values of the hyperparameter 7, Increasing y can improve unlearning efficacy (higher PUL) in some cases but may degrade sample quality (higher u-FID), and vice versa.
Table 4: PUL(f) and u-FID(4) for class unlearning on the MNIST, CIFAR-10, and tinylmageNet datasets for different values of y
Dataset
Unlesrued Classes
0.1
m 0.3
0.6
? = 0.8
PUL(%)
u-FID
PUL(%)
U-FID
PUL(%)
u-FID
PUL(%)
u-FID
Class-O
61.00%
65.25%
36.75
63.50%
62.00%
Class=
75.06%
14.43
72.15%
14.33
55.21%
11.54
71 71.67%
13.12
Class 2
69.08%
40.15
62.53%
33.50
65.84%
35.87
60.10%
38. 28.28
Class-3
43.70%
29.74
40.00%
31.86
44.20%
33.47
42.72%
36.95
MNIST
Class-6
50.52%
37.42
46.32%
38.35
57%1
48.61%
Class-7
40.90%
8.36
37%%
15.52
35.77%
36.70%
9.01
Class-8
68.96%
38.20
69.11
43.59
72.91%
41.68
74.23%
12.57
Class-9
44.43%
23.19
43.73%
26.98
48.49%
26.01
46.67%
29. 58
Clase-O O (airplane)
53.18%
28.93
48.96%
31.04
46.01%
30.66
39.55%
$2.34
Class-1 (Antommhile)
60.87%
18%
33.68
34.26
Class-6 (Frog)
63.98%
34.22
62.56%
30.17
70.04%
34.99
51 14.6
29.72
CIFAR-10
Class-7 (Horse)
41.81%
25.19
40.45%
23. 40
55.93%
21.09
48.36%
20.17
Clase-8 (Ship)
71.63%
24.46
74.65%
28.75
56.54%
20.51
69.95%
19.64
Class-9 (Truek)
44.60%
32.02
80%
34.50
41.00%
29.18
Class-O (Fish)
49.30%
27.56
56.67%
33.18
tinyImageNet
Class: 75 (Buteher Shop)
60. 10%
27.84
55.659E
21.17
66.67%
24.17
58.86%
20,92
Class- 125 (Soda Bottle)
50.00%
27.48
42.64%
18.16
51.60%
19.17
49.85%
23.15
A.2.2 Results on CelebA
Table compares our mothod with the bascline methods on unlcarning different features of the CelobA (Lu et al. 2015) dataset. VDU achieves the best u-FID across all features, indicating produces the highest- quality images post-unlearning, While ESD and SalUn often achieve higher comparable PUL, they suffer from extremely high u-FID scores, especially for Eyeglassos and Bangs (u-FID > 275), suggesting degraded image quality. VDU balances these metrics, offering significantly better visual fidelity while still achieving competitive PUL.
Experimental details for CclebA: For the pro-trained model, we have used the following open-source architecture implementation: https://github. cowm/tghh/dppn-oooogggoo (dpp-ttrrch and trained the model for 40 epochs with learning rate of 2-5 For this, T 1000 and batch size is taken to be 128. The pre-trained model has
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Table 5: PUL(1) and U-FID(U) for features unlearning on the CelebA dataset.
Fine-tuning
SalUn
ESD
VDU (Our Method)
Dataset
Unlearned Classes
PUL (%)
u-FID
PUL (%)
u-FID
PUL (%)
u-FID
PUL (%)
u-FID
Hats
83,56
11.73
37.67
98.17
38.34
82.18
43.56
27.46
CelebA
Eyeglasses
87.18
10.36
89.39
282.63
89.80
275.00
57.67
24.79
Bangs
85.52
12.75
67.87
310.31
67.50
299.37
46.65
23.17
FID of 17.82. For the unlearning, we achieve the optimal results using 7 = 0.3 just for 2 epochs of training with our method.
A.2.3 Class Unlearned Samples using VDU
Visual results of the original images and unlearned images for various class unlearning settings on the MNIST, CIFAR-10, and tiny ImtgeNee datasets are displayed in Figure produces images of high quality.
It can be seen that after unlearning, VDU
(a) Original
(b) Unlearn Digit '0'
(s) Unlearn Digit '1"
(2) Unlearn Digit
18"
2
7
6 3
7 7 8
S
7 6
6 0
7 3
1
/
5
MNIST
4
4
3
2
4
7
7
9
7
6 6 4
9
6
3
6
2-
7
5
5
4
4
2 6 8
1
5
1
3
9
5
8 5 4 9
8 0
2 7 6 O
4
1
7
0
1
7
9 7
5 2
4
7
5
3
5
5
4
7 9
3
6
7
/
5
/ 5
45354 66
5
3
9
(e) Original
(1) Unlearn 'Audomobile'
(g) Unlearn 'Frog'
(b)
Unlearn 'Ship'
CIFAR-LO
(8) Original
i Unlearm 'Fish'
(k) Unlearn Buttheer Shop
(1) Unlearn 'Soda Bottle'
tinyImageNet
Figure 7: Generated samples from the pre-trained DDPM model and different class unlearned models. Our method shows superior image quality after unlearning.
A.2.4 Feature Unlearned Samples using VDU
Visual results of the original images and unlearned images over various epochs for various fcature unlcarning settings, such as 'artistic style' and 'a particular object' from Stable Diffussin model pre-trained on the LAION-5B (Schuhmann et al. 2022) dataset,, are depicted in Figure and Figure g respectively. Results of unlearning "Van Gogh style' from Figure X show that given prompt related to the generation of 'Van Gogh' style images, the unlearned model doesn't 't generate such artistic style. Similarly, results for unlearning 'car' object are also depicted in Figure Visual results below show VDU's progress over multiple epochs during the unlearning. This kind of object removal has multiple use cases in computer vision-related tasks.
To further evaluate feature unlearning in Stable Diffusion, we compute CLIP similarity scores between the text prompt and the generated image, both before and after unlearning. Effeetiive feature suppression is
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Unlearning Concept "Van_ Van_Goghh
Prompt barn on quiet farm the style van gogh"
Original
Unlearned
Unlearned
Unleaming Concept *Van_ Van_Gogh"
Prompt "a busy street the style of van gagh"
Original
Unlearmed epociy-1
Unlearned
Unlearned epochi-3
Unlearned epociydd
warnee epoch-m5
epach-2
Unleaming Concept *Van "Van_Gogh"
Prompt "a farm in style van gogh"
G00
600
Original
Unlearned
Uniearned
Unlearned
Unleaming Concept Dan_Gogh"
Prompt "a forest in the style of gogh"
Original
Unlearned epoci--1
Unlearned epoch-2
Unlearred epoch-3
Unlearned epociymd
earrered epoch-
Unleaming Concept *Van Van_Goghh
Prompt sunrise the style of van gogh*
Original
Unlearned epoch-1
Unlearned
Unlearned epoch-3
Unlearned
leerned
Figure 8: Results of VDU on unlearning Van Gogh style' over multiple epochs
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Unlearming Concept "Car"
Prompt 'a car going downhill"
Original
Unleamed spoche]
Unleamed spochm2
Unleamed spoches
Unleamed spoche4
Unleamed spoches
Unleamed spochi6
Unleamed spochm
Unleamed spochim
unleamed spocheg
Unleamed spochi 10
Unlearming Concept
"Car"
Prompt
"a car going uphill"
Original
Unleamed
apoch=2
opoch=4
epach-
@poch-
spoch-
epoch-@
epoch- 10
Unlearming Concept
"Car"
Prompt "a car in the mountains"
Original
Unleamed
Unleamed
Unleamed
Unllaaeed
Unleamed Unleariing Concept "Car"
Unleamedd
Unleameed
Unneameed
Linleamed
Unleamed
Prompt car near tunnel"
Original
Unlcamed spoch]
Unlcamed spoch=2
Unlcamed epoch=3
Unleamed spochi4
Unleamed epochis
Unicamed epoch-6
Unlcamed epoch=?
Unleamed spoch=8
Unleamed epoch-9
Unlcamed epoch-
Figure 9: Rosults of VDU unlearning 'car object' over multiple epochs
Unlearning Concept 'Thomas Kinkade
"homas_Kinkade"
Prompt classic country farmhouse surrounded sunflowers by thomas kinkade"
Original
Unleamed spoch= 1
Unleamed esoch=2
Unleamed spoch=3
Unlearned epoche4
Unleamed epoch=5
Unleaming Concept Thooas Kinkade"
Prompt 'thomas kinkade inspired depiction of gazebo in bloaming garden"
Original
Unlearned sooch=1
Unlearned eooch-2
Unleamed spoch-3
Unlearned sooched
Unleamned esoche
Figure 10: Results of VDU unlearning the artistic style of 'Thomas Kinkade' over multiple epochs
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expected to result in reduced CLIP score after unlearning. We use the pretrained CLIP ViT-B/31 model to extract image-text representations and compute the similarity scores. As shown in Table 6 the CLIP scores consistently decrease after unlearning, indicating successful suppression of the targeted features. Here for artistic style we report the clip score after 5th epoch os unlearning and for object after 10 the opoch of unlearning. We also see a consistent decrease of score over the epochs indicating a steady suppression of features as epochs increase.
Table 6: CLIP scores before and after unlearning for different feature types.
Feature Type
Prompt
Original Image
Unlearned Image
barn on quiet farm in the style of van Gogh
0.3582
0.2593
Artistic Style
a farm in the style of van Gogh
0.3364
0.2482
sunset in the style of van Gogh
0.3477
0.2212
going downhill a car in the mountains
0.2729
0.2132
Object
0.2976
0.2136
A.3 Further Discussions
A.3.1
Minimization of Lower Bound
Notice that Theorem establishes lower bound to our variational objective which is minimized in our proposed loss function. In general, there is no theoretical guarantec that minimizing the derived lower bound necessarily minimizes the original objective. However, it is important to note that this lower bound arises exclusively from the application of Lemma 1, which corresponds to the Evidence Lower Bound (ELBO) formulation for diffusion models. In general, the ELBO becomes tight only when the model is sufficiently well trained and can be assumed to accurately represent the underlying data distribution. Under this assumption, minimizing the E.BOO serves meaningful proxy for minimizing the original objective. Consequently, our experimental goal is to demonstrate that, despite optimizing lower bound in the loss function, the method still achieves the desired unlearning objective in practice.
A.3.2 Estimation of μ and of
As can be seen from our method's formulation, we require the model parameters' mean (pf) and variance (of), which can only be obtained from multiple independent training checkpoints. So we train 5 models independently on each of the datasets calculate μ and of for MNIST, CIFAR-10, and tinylmageNet datasets. Since pre-trained checkpoints 0* essentially samples from P(0) P, Dy), i.c. H" ~ P(0 D,, Dy), according to the Bayesian inference [Blundell et al., 2015) formulation, these can be estimated from the empirical mean and variance of multiple independent training checkpoints of the pre-trained model. Therefore, by varying the number of checkpoints achieved from independent trainings, Table shows that our approach appears to be robust and effective even with a relatively small number of independent training checkpoints.
Table 7: Impact of the number of checkpoints from multiple independent training runs
Table 8: Impact of the number of checkpoints from a single training run
MNIST (Digit-1)
CIFAR-10 (Ship)
EN (Buteher Shop)
MNIST
CIFAR-10 (Ship)
tIN (Clnss-75)
# Checkpoints
# Checkpoints
(Digit-1)
PUL w-FID
PUL
u-FID
PUL
u-FID
PUL
u-FID
PUL
u-FID
PUL
u-FID
75.54
13.12
72.23
28.98
62.36
26.74
73.12
12.65
70.53
32.02
58.75
70.46
12.34
70.22
30.16
62.00
26.56
3
66.53
10.47
65.89
33.27
60.12
26.73
77.97
13.22
74.65
28.75
65.86
26.47
12.23
72.67
63.36
Necessity regarding multiple independent checkpoints: We acknowledge that the necessity of chockpoints from multiple indopendent training to estimate μ4 and of could be a limiting factor of VDU. To get around this problem, we estimate jf and of by saving several checkpoints from single training run during the final few iterations. Even though theoretically these checkpoints are not independent samples
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from P,, Dy), practically this seems to work (with slight degradation) shown in Table Also, we believe that this is more realistic because, in general, we save several checkpoints during single training run. In fact this is done for all the experiments in Stable Diffusson. As it is practically hard to run such large-scale models independently multiple times, we use multiple checkpoints the Stable-diffusion model from a single training run. Figure and Figure prove that VDU effective more practical scenarios.
In both of these configurations (Table and Table B we maintain y the optimal values, which are 7 0.1 for MNIST, ? 0.3 for CIFAR-10, and y 0.6 for tinylmageNet.
A.3.3 Computational and Memory cost
VDU's computational and memory cost: The computational cost and memory usage depend on datasets and modcls. We used two Nvidia A6000 (48 GB GPU) to all experiments. On the MNIST dataset, per epoch unlearning lakes around 50 secs, on CIFAR-10 210 secs, and tiny ImageNet takes around 300 secs per epoch. Now, the main memory usage for VDU comes from saving multiple checkpoints. For MNIST per chockpoint takes memory of 40 MB, for CIFAR-10, 200 MB, for tinylmageNet 450 MB per checkpoint, and for CelebA, it is 560 Mb per checkpoint. For Stable Diffusion, the memory usage each pre-trained checkpoint 3.97 GB.
Computational Time Comparison Across Unlearming Methods
Finstusing
Computatin Time (epochs)
ESD
Table 9: Time taken to unlearn for epoch (in seconds) across datasets.
Dataset
VDU
SA
SalUN
ESD
MNIST
50
540
63
68
CIFAR-10
210
588
230
227
tinylmageNet
300
612
489
471
CHAAR110
Ennylngefieet
Dalasets
Figure 11: Unlearning time (epochs) using different methods. VDU takes comparatively fewer epochs than other baselines.
Comparison with basclines: The computing time (in epochs) needed by various unlcarning techniques on four datasets MNIST, CIFAR-10, Tiny Imnylmag,ee,, and CelebA is contrasted in Figure 11 Fine-tuning (blue)
has the lowest computational cost but is ineffective when the inaccessible non see--ulllaanngggg class dataset (D,).
datasets, VDU (purple bars) consistently uses fewer epochs than ESD (Gandikota et al. 2023b) (red) and SalUn (Fan et al., 2024) (green), and comparable epochs as SA (Heng & Soh 2023). VDU an effective unlearning technique that drastically lowers the number of epochs needed without sacrificing performance. This makes it sensible option for practical uses when computational cost is crucial consideration.
A.3.4 Discussion on experimental settings
Restriction of access to the samples from D,: In all of our experimental settings, don't assume access to samples (original from training data generated by the pre-trained model) from D,. The primary motivation for this restriction is that we experimentally demonstrate, simply Fine-tuning with samples from D, (provided we have access to data from D,) is the optimal technique (Ref. third column of Table 1) that produces the best results with the least amount of computing (with only one epoch). Thus, from a practical perspective, all the unlcarning methods are only useful when we are restricted using samples from D,.. For this reason, we remove generative replay from Selective Amnesia (SA) method, and the loss components pertaining to D, also removed from SalUn and ESD methods.
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Table 10: Comparison unlearning performance with additional fine-tuning using a small subset of D,..
Selective Amnesia
SalUn
ESD
VDU
0.3)
Dataset
Unlearned Class
PUL(%)
u-FID
PUL(%)
u-FID
PUL(%)
u-FID
PUL(%)
u-FID
MINIST CIFAR-10
Digit-1 Automobile
33.64
108.76
69.87
31.67
72.86
25.38
89.08
7.46
18.67
74.12
16.87
59.19
12.08
62.65
72.56
22.02
tinyluageNet
Fish
69.83
31.86
44.59
40.92
43.87
42.15
62.96
25.82
To further analyze performance under limited access to samples from Dr: we report additional results in Table 10. In this setting, we fine-tune the unlearned model for epoch using a restricted subset of Dr, consisting of only 50 samples per class. The results demonstrate that even limited fine-tuning on D, consistently improves performance across all methods, and VDU gives relatively superior to comparative performance in this setting also.
Restriction of Unlearning epochs: Note that the unlearning algorithm's main goal is to emulate the retraining method that uses samples only D, while being computationally efficient. Tf the unlearning process takes long time, especially more than retraining, it effectively defeats the purpose of proposing such algorithms. In this case, if assume finetuning with samples from D, is feasible, then it is the optimal method both in terms of proposed metrics and compulational elficiency (Ref. column 3 in Table 1). Finetuning with D, achieves optimal results just with 1 epoch (very few iteration depending upon the batch size). We only train all methods for very few epochs (10x of fine-tuning time) in order to consider computational efficiency and choose the best method that requires the fewest iterations.
A.3.5 Methodological comparison between SA and VDU
SA method depends on the importance-based penalty using Fisher Information Matrix (FIM), which is avoided in our case with the use of stability regularizer. With the stability regularizer, each parameter is weighted proportionally to ( However, the FIM-based penalty is inherently data-dependent. Specifically, when limited to the unlcarning data subset Dy; the calculation of the FIM in SA method does not account for the importance of the weights in retaining the information of D,. Consequently, the model forgets the retaining data subset, leading to the generation of low-quality samples (high u-FID scores) even though it performs well in terms of PUT scores.
A.3.6 Feature entanglement between D, and Dy
In complex datasets due to high entanglement between features, it is really challenging unlearn a particular specific feature while preserving others. As any machine unlearning approach will unlearn data-level knowledge, the unlearned model will forget some part of the entangled fcatures as well if D, and D, overlap. This will have an impact on the unlearning quality (u-FID scores). If there is feature overlap between the samples from D, and Dy, the unlearned model will forget some of the common features because the goal of any machine learning technique is to forget all the data-level information. For example, in feature unlearning from pre-trained Stable Diffusion models, we can visually inspoct from Figure 7 and Figure g that during the unlearning of artistic styles and objects, image quality is impacted bit. This emphasizes for possibilities for better methodologies as part of future work.
A.4
Implementation Details
A.4.1 Datasets and Models
The MNIST dataset consist of 28x28 grayscale representing handwritten digits from 0 to The MNIST dataset contains 60,000 training images and 10,000 testing images. We have used the same architectural model detailed in the open-source implementation: httpps//giithbb.co explainingai- watpaaaa-ccoooDDD--PPtPtoooo
MNIST:
(Ronneberger et al. 2015) for the MNIST dataset.
CIFAR-10: CIFAR-10 consists of 60,000 color images of size 32 distributed across 10 classes with 6000 images in each class. We adopt unconditional DDPM model based the approach by
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Published in Transactions on Machine Learning Research (03/2026)
Nichol & Dhariwal 2021]. p. utilizing their official implementation provided in https:///ithubb.cm
openai/taproved-diffee ditddddiffusiiii
tinyImageNet:
This contains 100000 images of 200 classes (500 for each class) downsized to 64 colored images. Each class has 500 training images, 50 validation images and 50 test images. We adopt an unconditional DDPM model based on the approach by (Nichol & Dhariwal 2021 utilizing their official implementation provided in
diffusion
LAION-5B:
This is the largest public image-text dataset, containing over 5.8 billion samples. More details on this dataset can be found here: https://aaio..a//ppoopoooo use a state-of-the-art Stable Diffusion model. Details of the architecture can be found in the open source implementation at: htttpp///gggaaaaocoo/////////aae
For this experiment, we
A.4.2 Pre- Tre-Training
For the pre-training of the DDPM model on MNIST, we adopt the hyperparameters from the open source code base mentioned above. Specifically, a randomly initialized DDPM model is pre-trained on the train set of MNIST and optimized using a learning rate of 10 for 40 epochs with a batch size of 64. The diffusion process follows linear noise scheduling strategy with dn 0.0001 and or = 0.02 at the final time-slep 100000. We have trained 5 models to get the model mean p and variance of parameter.
MNIST:
CIFAR-10: We use unconditional DDPM checkpoint, pre-trained on CIFAR-10, from https ; //github. //gibubb.ccm/ppea////mppe.
We fine-tune this model on the train set of CIFAR-10 10 for 90k iterations, with batch size of 128, and learning rate of 10-5, The total diffusion steps T 4000 with a cosine noise scheduling strategy with 0.0002 and or 0.04. Here, we have trained 4 models to get the model mean je and variance of parameters. For the pre-training of both DDPM models, we use Adam optimizer.
LinyImageNNet: We use unconditional DDPM checkpoint, pre-trained on LinylmageNet, from We finc-tune this model on the train set of linylmageNee for 70k iterations, with a batch size of 64, and a learning rale of 10-6, The total diffusion steps T = 4000 with a cosine noise scheduling strategy with on = 0.0002 and or = 0.04. Here, we have trained 5 models to get the model mean 14 and variance of parameters. For the pre-training of both DDPM models, we use the Adam optimizer.
https://github. com/ httpa///immoovedddfffeee
For this, we didn't train the Stable Diffusion models but used the open-source These checkpoints are trained with a linear noise scheduling strategy from on = 0.00085 to aT = 0.0120 with T 1000 and learning rate 10-4 We have used four checkpoints that are present in the repository: sd-v1- 1.ckpt, sd-v1-2.ckpt, sd-v1-3 sd-v1-3.ckpt, sd-v1-4.ckpt.
LAION-5B:
checkpoints available at: https://github: hatps://githhbb..om//mm/iiiissst www.////o//////eeeeooeeees wttp:///////////ttaleeeedodo httpp//iisssaabeeedffuiiiooooooi
A.4.3 Unlearning
After pre-training the DDPM models their respective datasets, described carlier, we now outline the unlearning process for each. We optimize using our proposed loss function, as defined in Eq. 2 ensuring effective fcature removal while maintaining model performance. Note that during the unlcarning phase, for all the datasets, the noise scheduler is kept the same as in the pre-training phase.
1. MNIST: The model is optimized for unlcarning over only 1 epoch using the Adam optimizer with a learning rate of 10-6 and a batch size of 128.
2. CIFAR-10: The model is optimized for unlearning over epochs using the Adam optimizer with learning rate of 10-6 and a batch size of 128.
tinylmageNet: The model is optimized for unlearning over only epochs using the Adam optimizer with learning rate of 10-6 and batch size of 128.
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Published in Transactions on Machine Learning Research (03/2026)
4. LAION-5B: Note that, don't have access to the labels in this dataset to obtain Dy, we generate samples from D by prompting ChatGPT and passing these prompts to a model initialized with checkpoint sd-vl-1.ckpt. We only generated 650 samples corresponding to Dy for both 'artistic style' and 'object' unlcarning scttings. Here we have used Adam optimizer with a learning rate of 10-6.
A.4.4 Additional Details
Hyper-parametts details: For all of the benchmark datasets, we select and report the results for y E (0.1, 0.3, 0.6, 0.8). We achieve optimal experimental results using 7=0.1 and 0.6 for all the classes on MNIST and tinylmageNet, respectively. On CIFAR-10, choose optimal of 0.1 for unlcarning "Automobile" and "Ship'. For "Frog", use 7-0.3. For feature unlearning in the LAION-5B dataset, we have set 7 0.6.
Classifier Details: To calculate u-FID and PUL metrics from unconditional Diffusion models, we need samples that correspond to D, part of the training data. Thus, we classify samples that relate to D, by pre-trained models. We trained a ResNet-50 model with an accuracy 99% for MNIST, a 1enseNet-121 with an accuracy of 92% for CIFAR-10, ViT-B16 with an accuracy of 98% for tinylmageNet, and ResNet-50 with accuracy of 81% for the CelebA dataset.
Code: Our implemeniation can be found al: https://github. cow/Suubodip113/// 1 this repository as we keep updating with more implementation details and results.
Keep referring to
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Reviews:
[{"review_id": "XYflRX5YFm", "reviewer": "Reviewer_7yLg", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "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": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper addresses the challenge of machine unlearning in diffusion models under data-constrained settings where the full training dataset is inaccessible, proposing Variational Diffusion Unlearning (VDU), which leverages a variational inference framework with a loss function consisting of a plasticity inducer (minimizing log-likelihood of undesired data) and a stability regularizer (preserving pre-trained parameters); it is validated through comprehensive experiments on class unlearning (MNIST, CIFAR-10, tinyImageNet) and feature unlearning (Stable Diffusion), achieving high PUL and low u-FID, while being computationally efficient, requiring only access to the undesired data subset, and effectively balancing unlearning effectiveness and generation quality.", "claims_and_evidence_yn": "Yes", "claims_explanation": "VDU mathematically formulates unlearning as variational divergence minimization, with a loss function that combines a plasticity inducer (minimizing undesired data log-likelihood) and a stability regularizer, derived from the KL-divergence between the variational posterior and the pre-trained parameters.  Experimentally, VDU achieves high PUL and low u-FID across class unlearning and feature unlearning, outperforming baselines.", "audience_yn": "Yes", "audience_explanation": "This study aims to restrict the model from learning certain content, which holds significant value for practical applications by preventing the model from generating unhealthy material.", "requested_changes": "Quantitative Metrics for Feature Unlearning in Stable Diffusion: While Figure 1 qualitatively shows \"Van Gogh style\" unlearning over epochs, the paper lacks quantitative metrics to measure feature suppression (e.g., style similarity scores using pre-trained style extractors like VGG or CLIP, or text-image alignment metrics for \"Car object\" unlearning). Without numerical benchmarks, it is unclear if residual style/feature traces remain. The authors could supplement qualitative results with quantitative metrics (e.g., style cosine similarity between original and unlearned outputs) to validate feature unlearning effectiveness.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "FNr3tnfVBb", "reviewer": "Reviewer_Grhj", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "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": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes Variational Diffusion Unlearning (VDU), a data efficient method for machine unlearning in diffusion models (DM) built upon the Variational Bayesian Unlearning framework in [1]. More precisely, similarly to [1], VDU minimizes the variational KL-divergence $D_{\\text{KL}}(q(\\theta)|p(\\theta|D_r))$ between the learnable approximate posterior $q(\\theta)$ and the true posterior $p(\\theta|D_r)$ defined via the Bayes’ theorem. Here $D_r$ denotes the retain set. As in [1], this KL-divergence is represented as a sum of two terms: the log likelihood of the forget set $D_f$ and the KL-divergence between the learnable approximate posterior belief $q(\\theta)$ and the fixed approximate posterior belief $p(\\theta|D_r, D_f)$. \n\nThe authors propose to model both $q(\\theta) \\sim \\prod_i \\mathcal{N}(\\theta_i, \\sigma_i^{\\*2})$  and $p(\\theta|D_r, D_f) \\sim \\prod_i \\mathcal{N}(\\mu_i^{\\*},\\sigma_i^{\\*2})$ as factorised Gaussians with the shared variance $\\sigma_i^{\\*2}$. Parameters $\\mu_i^{\\*}$ and $\\sigma_i^{\\*2}$ are estimated by computing statistics of either the final checkpoints of $N$ independent runs, or $N$ late checkpoints of the same run.\n\nFinally, the authors derive a lower bound on their likelihood term, which results in the lower bound on the initial variational KL-divergence $D_{\\text{KL}}(q(\\theta)|p(\\theta|D_r))$ minimized w.r.t. $\\theta$.\n\nVDU is evaluated in the class unlearning setting on MNIST, CIFAR-10 and tinyImageNet using unconditional DDPM, and in the feature unlearning setting on LAION-5B using Stable Diffusion. In the setting where $D_r$ is unavailable, the proposed method outperforms Selective Amnesia (SA), Saliency Unlearning (SalUn) and Erasing Stable Diffusion (ESD).\n\n**Strengths**:\n- For the most part, the paper is well-written, and individual sections are easy to follow.\n- Data efficiency: relying only on the forget set $D_f$ might be beneficial when there is no access to the retain set $D_r$.\n- VDU outperforms the considered baselines in terms of Percentage of Unlearning (PUL, measures unlearning quality) and Unlearned Fréchet Inception Distance (u-FID, measures utility preservation).\n\n**Weaknesses**:\n- [Major] The claim about “the establishment of a theoretical connection between the problem of machine unlearning and variational inference” being a key contribution is somewhat misleading since representation of the problem as approximate Bayesian unlearning has been explored before, notably in [1], which the authors acknowledge to be inspired by (see Sec. 3.2). \n- [Major] The authors propose to minimize the *lower* bound on the variational KL-divergence $D_{\\text{KL}}(q(\\theta)|p(\\theta|D_r))$. Lower bound minimization does not guarantee that the function of interest is actually minimized unless you can bound the gap between the lower bound and this function. This weakens the claim about “the established theoretical connection” even more.\n- [Major] The logic of model presentation is hard to follow. For full derivation of the final loss in Eq. (2), the reader has to go back and forth between different following sections in the main paper and in the appendix, sometimes not even in the order of appearance. This negatively affects the readability of the paper.\n- [Major] Several benchmarks for DM unlearning are missing, such as ConceptBench [2], UnlearnCanvas [3] or I2P.\n- [Major] Qualitative results on Celeb-A are missing. Qualitative results for all baselines and all benchmarks are also missing. This makes it impossible to comprehensively evaluate the performance of different approaches. \n- [Minor] Qualitative results of object unlearning for Stable Diffusion in Figures 4 and 9 are not convincing and demonstrate significant degradation in the quality of generated images.\n- [Minor] The proposed method lacks flexibility and does not scale straightforwardly when the retain set $D_r$ is available, at least partially.\n\n[1] Nguyen Q.P. et al. “Variational Bayesian Unlearning”. In NeurIPS, 2020.\n\n[2] Zhang E. et al. “Forget-Me-Not: Learning to Forget in Text-to-Image Diffusion Models”. In arXiv preprint arXiv:2211.08332, 2023.\n\n[3] Zhang Y. et al. “UnlearnCanvas: Stylized Image Dataset for Enhanced Machine Unlearning Evaluation in Diffusion Models”. In NeurIPS, 2024.", "claims_and_evidence_yn": "Yes", "claims_explanation": "Overall, the claims made in the submission are supported reasonably well. The paper indeed proposes a data-efficient method for DM unlearning that requires access only to the forget set $D_f$, and this method is evaluated in the class-unlearning setup on DDPM and in the feature-unlearning setup on Stable Diffusion. However, according to the authors, the key contribution of the paper is supposed to be “the establishment of a theoretical connection between the problem of machine unlearning and variational inference”, which is a misleading claim for two reasons: 1) the same approximate Bayesian unlearning framework has already been proposed in prior works (as mentioned above), and 2) the resulting objective function does not guarantee minimization of the function for which this theoretical connection has been established.", "audience_yn": "Yes", "audience_explanation": "The problem of machine unlearning has been attracting a lot of attention recently, motivated by a number of use cases including privacy regulation or content moderation. The findings of this paper can potentially be of use to the community of researchers interested in machine unlearning for DMs in data restricted scenarios when only the “to-be-removed” data is available.", "requested_changes": "**Major issues**:\n- I would recommend rewriting the claims regarding the theoretical connection between machine unlearning and variational inference as a major contribution, especially since derivation of the variational KL-divergence is not new [1], and since the final loss in Eq. (2) does not guarantee to minimise the desired objective (variational KL-divergence). Alternatively, the authors could provide theoretical proofs that such a guarantee exists.\n- The readability of the paper could be significantly improved by changing the order of sections and, as a results, the order of equations. In the current version, the general formulation of the problem in Eq. (1) is immediately followed by the final version of the loss in Eq. (2), without proper annotation of variables and/or parameters which are introduced much later. The order of derivation, however, seems to be as follows: Eq.(1) -> Eq. (51-51) in Sec. A.1.3 -> Lemmas 1 and 2 in Sec. 3.3 -> proofs in Sec. A.1.1. and Sec. A.1.2.3, etc. Some equations (e.g., Eq. (51-54) in Sec. A.1.3) could be moved to the main paper for more seamless flow of information.\n- To strengthen the claims about data efficiency, it would be interesting to see comparison between VDU and SA, SalUn and ESD when the latter have access to a small subset of $D_r$ (e.g., to a random subset). Reusing only a small fraction of $D_r$ can still be considered *data efficient* and should not be ignored. \n- On each benchmark, it would be interesting to see qualitative comparison with all the baselines to better understand how well u-FID metric captures degradation in image quality. \n- Quantitative results lack comparison with the “gold” model, i.e., the model that has been trained from scratch only on $D_r$. Even though this baseline is computationally inefficient, I think the community would benefit from seeing the “upper bound” on the considered metrics.\n- The paper would benefit from a more comprehensive evaluation on recent benchmarks (ConceptBench [2], UnlearnCanvas [3], I2P).\n\n\n\n**Minor issues**:\n- The purpose of Algorithm 1 is not clear, as it describes the standard SGD update. It could be removed, and the free space could be used for equations and/or sections from the appendix that are more critical for understanding the paper.\n- A number of equations are not numerated (both in the main paper and in the appendix). Adding numeration would simplify referencing and discussion about the content of the paper.\n- It is not clear how the learned approximate posterior belief $q(\\theta)$ is used in practice: do you use the mean $\\theta$ in $q(\\theta) \\sim \\mathcal{N}(\\theta, \\sigma^{*2})$ as the parameters of the unlearned model or do you sample from this distribution?\n- It would be interesting to see how sensitive are VDU and the baselines to the number of unlearning epochs. This parameter seems to be important for VDU since the first term in Eq. (2) is unbounded, so I wonder if eventually it overpowers the second term.\n- In Sec. 4.3, why is there a need to use a classifier “to remove unlearning data from the real data”? Usually D_f is provided, so obtaining D_r is trivial. Maybe the authors meant something else, this should be clarified.\n- The order of the columns (metrics) in Tables 1 and 3 is different. The readability would improve if the order becomes the same.\n- The reference “Zoubin Ghahramani and H. Attias. Online variational bayesian learning. *Workshop on Online Learning*, NeurIPS, 2020.” does not seem to exist (to the best of my knowledge, there were no workshops with such a title at NeurIPS in 2020). Please, verify that the references are correct.\n\n\n[1] Nguyen Q.P. et al. “Variational Bayesian Unlearning”. In NeurIPS, 2020.\n\n[2] Zhang E. et al. “Forget-Me-Not: Learning to Forget in Text-to-Image Diffusion Models”. In arXiv preprint arXiv:2211.08332, 2023.\n\n[3] Zhang Y. et al. “UnlearnCanvas: Stylized Image Dataset for Enhanced Machine Unlearning Evaluation in Diffusion Models”. In NeurIPS, 2024.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "raQ3Ybxoij", "reviewer": "Reviewer_igS7", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "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": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper is on unlearning in the context of (image) diffusion models in the setting where the original pertaining dataset is not accessible.\nTheir method, based on variational inference, attempts to optimize an objective consisting of two terms -- The first term (plasticity inducer) reduces the likelihood of the undesirable points, and the second term (stability regularizer) works to maintain the quality of generations. \nThis is in contrast to several current methods which instead either require access to the entire training set, or rely on synthesizing fake data to retrain the model. \n\nThe the paper shows:\n1. A theoretical guarantee demonstrating that under the gaussian mean-field approximation in parameter space, the ELBO may be lower bounded by the appropriate objective consisting of the plasticity inducer and stability regularizer.\n2. They propose a novel algorithm (VDU) that optimizes the above objective to find a model which has forgotten the desired information. \n2. Evidence on various image datasets of unlearning.", "claims_and_evidence_yn": "Yes", "claims_explanation": "There are 5 claims made in the paper:\n\n1. Mathematical derivation of the claim that unlearning can be modeled as a VI problem. They demonstrate this with proof in the Gaussian mean-field approximation setting\n\n2. VDU does not need the original dataset to forget the information. They provide experiments on CIFAR-10 and CelebA-HQ. They measure the FID on the retain class, and this remains low, wheras baseline show a spike in FID when retain data is missing. \n\n3. VDU provides convergence in one-epoch and has superior efficiency. The paper plots \"Forgetting score\" vs \"training steps\" and these show that the forgetting metric plateaus early in the training process. \n\n4. VDU achieves disentangled learning. The authors claim that their method can erase a specific style or object without damaging closely related concepts. *evidence for this is a little weaker than the rest*, because the specific classes like Van Gogh vs Church etc seem fairly distinct. It would be nicer if they provided evidence of the concepts being very related and still remaining unaffected (i.e. the paper fails to provide strong evidence for highly entangled concepts).", "audience_yn": "Yes", "audience_explanation": "This is a paper on diffusion models and unlearning, and will be of relatively high interest to the TMLR audience. The current evidence is only strong for some kind of coarse disentanglement.", "requested_changes": "It would be good to provide more evidence for the effect of VDU on entangled concepts (such as wheels and cars)", "broader_impact_concerns": "None", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)