Self-Consuming Generative Models Go MAD
Authors: Sina Alemohammad
Josue Casco-Rodriguez
Lorenzo Luzi
Ahmed Imtiaz Humayun
Hossein Babaei
Daniel LeJeune
Ali Siahkoohi
Richard Baraniuk
Venue: ICLR 2024 poster (2024)
Keywords: Generative Models
Synthetic Data
Sampling Bias
Diffusion Models
GANs
Primary area: generative models
TL;DR: We show that generative models recursively trained on synthetic data are doomed to have their quality or diversity progressively decrease.

Abstract: Seismic advances in generative AI algorithms for imagery, text, and other data types have led to the temptation to use AI-synthesized data to train next-generation models. Repeating this process creates an autophagous ("self-consuming") loop  whose properties are poorly understood. We conduct a thorough analytical and empirical analysis using state-of-the-art generative image models of three families of autophagous loops that differ in how fixed or fresh real training data is available through the generations of training and whether the samples from previous-generation models have been biased to trade off data quality versus diversity.  Our primary conclusion across all scenarios is that *without enough fresh real data in each generation of an autophagous loop, future generative models are doomed to have their quality (precision) or diversity (recall) progressively decrease.* We term this condition Model Autophagy Disorder (MAD), by analogy to mad cow disease, and show that appreciable MADness arises in just a few generations.

Published as a conference paper at ICLR 2024
SELF-CONSUMING GENERATIVE MODELS Go MAD
Sina Alemohammad," Josue Casco-Rodriguees Lorenzo Luzi, Ahmed Imtiaz Humayun?
Hossein Babaei, Daniel LeJeune; Ali Siahkoohi, Richard G. Baraniuk!
DDpartment of ECE, Rice University; 'Dpaarment of Statistics, Stanford University;
Department CMOR, Rice University
ABSTRACT
Seismic advances in generative AI algorithms for imagery. text, and other data types have led to the temptation to use Al-synthesized data train next-generation models. Repeating this process creates an autophagous ("self-consuming)) loop whose properties are poorly understood. We conduct a thorough analytical and empirical analysis using state-of-the-an generative image models of three fam- ilies of autophagous loops that differ in how fixed or fresh real training data is available through the generations of training and whether the samples from previous-generatiin models have been biased to trade off data quality versus di- versity. Our primary conclusion across all scenarios is that without enough fresh real data in each generation of an autophagous loop, future generative models are doomed to have their quality (precision) diversity (recall) progressively decrease. We term this condition Model Autophagy Disorder (MAD), by analogy to mad cow disease, and show that appreciable MADness arises just few generations.
Generation t =
t=
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Training generative artificial intelligence (AI) models on synthetic data progressively amplifies artifacts. As Al-synthesized data proliferates in standard datasets and the Internet, future Al models will train on both real and synthetic data, forming autophagous ("self-consuming" loops. We highlight potential unintended consequence of autophagous training. We trained sequence of StyleGAN2 (Karras et al., 2019a) models wherein the model at generation 2 2 trains only on data synthesized by the model generation t 1. This forms fully synthetic loop (Figure 3) without sampling bias (A = 1). Note how the cross cross-hatches hatched artifacts (possibly an architectural fingerprint (Karras et al., 2021)) are progressively amplified each generation. Appendix D has more samples.
Figure 1:
INTRODUCTION
Synthetic data' from generative artificial intelligence (Al) models like Stable Diffusion (Rombach al., 2022) and ChatGPT (OpenAl, 2023) is rapidly proliferating on the Internet. Indeed, there will soon be much more synthetic data than real data on the Internet.
Equal contribution.
By "synthetic" we Al-synthesized data, opposed data synthesized via physics-based simulations.

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Figure 2: Today's large-scale image training datasets contain Al-generated data. Datasets like LAION-5B (Schuhmann et al., 2022), which trains popular models like Stable Diffusion (Rombach et al., 2022), contain Al-synthesized images. Here are LAION-5B (haveibeentrained.com containing data synthesized by (left to right) AICAN (Elgammal al., 2017). Pix2Pix (Isola et al., 2017). StyleGAN (Karras et al., 2019a), and DALL-E (Ramesh et al., 2021). Generative models using LAION-5B thus close an autophagous ("self-consuningg) loop (see Figure 3) that can progressively amplify artifacts (Figure 1) and lower quality (precision) and diversity (recall).
samples
Since the training datasets for generative Al models tend be sourced from the Internet, today's Al models are unwittingly being trained on increasing amounts of Al-synthesized data. Figure 2 confirms that the popular LAION-5B dataset (Schuhmann et al., 2022), used train state-of-the-art models like Stable Diffusion, contains synthetic images from several earlier generations of generative models. Al generating formerly numan-sourced data, like reviews (Gault, 2023), websites (Cantor, 2023), and data annotations (Veselovsky et al., 2023), often with no indication of its origin (Christian, 2023). As the use of generative models continues to grow rapidly, this situation will only accelerate.
Moreover, throwing caution to the wind, Al-synthesized data is increasingly used by choice for training because is convenient, especially in data-scarce applications like medicine (Pinaya et al., 2022) and geophysics (Deng et al., 2022), and because it can protect privacy (Luzi et al., 2024; Klemp et al., 2023) in sensitive data applications like medicine (Packhäuser et al., 2022: DuMont Schütte et al., 2021). Most importantly,
deep learning models become increasingly enormous (Azizi et al., 2023; Burg et al., 2023), we are simply running out of real data on which to train them (Economist, 2023a;b; Villalobos et al., 2022).
The witting or unwitting use of synthetic data to train generative models departs from standard AI training practice in one important respect: repeating this process for generation after generation of models forms an autophagous ('self-consumingg)) loop (Figure 3). Different autophagous loop variations arise depending on how existing real and synthetic data are combined into future training sets. Additional variations arise depending on the model sampling biases used to trade off perceptual quality (fidelity or coherence) versus diversity (variety or heterogeneity)."
The potential ramifications of autophagous loops on the properties and performance of generative models poorly understood. In one direction, autophagy might progressively amplify the biases and artifacts present in any generative model as fingerprints. In Figure 1, autophagy progressively ampli- fies cross- hatshhat artifacts (reminiscent of aliasing (Karras et al., 2021)) in subsequent generations of StyleGAN2 models. In another direction, autophagous loops featuring generative models tuned to produce high quality syntheses at the expense of diversity (such as Karras et al. (2019a); Ho and Salimans (2021)) might progressively dilute the diversity of the data on the Internet." By analogy to mad cow disease (Nathanson et al., 1997), we term these and other symptoms of autophagy as Model Autophagy Disorder (MAD).
Contributions. We conduct a careful theoretical and empirical study of AI autophagy with generative image models. The concepts developed herein apply to any data type, including text. We also unify the results of contemporaneous work. Our three key contributions establish that, without enough fresh real data each generation, future generative models are doomed to go MAD. Moreover, we demonstrate that appreciable MADness can occur in only a handful of generations.
1. Realistic models for autophagous loops. We propose three families of self-consuming loops that realistically model how real and synthetic data are used to train generative models (recall Figure 3):
We quantify quality and diversity via precision and recall, respectively (Kynkäänniemi et al., 2019).
Similar to diversity exposure in recommender systems, where maximizing click rates discourages exposure diverse ideas (Stroud, 2011; Dylko al., 2017; Beam, 2014; Bakshy et al., 2015; O'Callaghan et al., 2015).
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Figure 3: Recursively training generative models on syn- thetic data from other models produces an autophagous "ssel--consuming)) loop. In this paper, we study three au- tophagous loop variants (defined in Section 2): the fully synthetic loop (only synthetic data), the synthetic augmenta- tion loop (synthetic + fixed real data), and the fresh data loop (synthetic fresh real data). Each generation samples with bias À that trades off sample quality versus diversity.
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The fully synthetic loop (Section 3), where the training dataset for each generation's 's model consists solely of synthetic data sampled from previous generations' models, such as by training a generative model on its own outputs (followfox.ai, 2023). We show that either the quality (precision) or the diversity (recall) of the generative models decreases over generations.
The synthetic augmentation loop (Section 4), where each generation's ' training data includes syntheses from previous generations and fixed set of real data, such as by training on real and self-generated data (Huang et al., 2022). We show that fixed real training data only delays the inevitable degradation of the quality or diversity of the generative models over generations.
The fresh data loop (Section 5), where each generation's 's training data includes syntheses from previous generations plus some fresh real data, which models the common practice of scraping the Internet for training data, which finds both real and synthetic data (recall Figure 2). We are the first to propose and study this flavor of autophagy. We show that, with enough fresh real data, model convergence is independent of initialization, with quality and diversity that do not degrade over generations.
Sampling bias plays a key rôle in autophagous loops. Practitioners often favor high-quality syntheses, whether through curation or automatic qivieiy-dvversity tradeoff's (Ho and Salimans, 2021; Karras et al., 2020). We show that, without these sampling biases, MADness degrades quality and diversity, while with them, quality be maintained but diversity degrades even faster.
3. Autophagous loop behaviors hold across a wide range of generative models and datasets, including Gaussian, Gaussian mixture, diffusion (DDPM, Ho et al., 2020), StyleGAN2 (Karras et al., 2020), Wasserstein GAN (WGAN, Gulrajani et al., 20) and Normalizing Flow (Kobyzev et al., 2020) models trained on datasets like FFHQ (Karras et al., 2019b) and MNIST (Deng, 2012).
Related work. We define a cohesive autophagy framework, supported empirically by state-of-the-an models, that unifies and significantly extends contemporaneous results that consider fragmented aspects of MADness. Shumailov et al. (2023) study autophagous loops without sampling bias and show that MADness ensues from variational autoencoders and Gaussian mixture models in fully synthetic and language models in synthetic augmentation loops. However, the absence of quality-diversity tradcoffs (sampling biases) in their models limits the applicability of their findings to real-world scenarios. Furthermore, in each generation they only fine-tune their language models, while we train our models from scratch. Martínez al. (2023a) also consider unbiased synthetic augmentation loops, but only show qualitative evidence of MADness on small dataset. Martínez et al. (2023b) focus only on fully synthetic loops and report that sampling bias can prevent degradation of image quality in small datasets. Finally, Huang et al. (2022); Hataya et al. (2022) and others have considered synthetic data augmentation, but not in the context of autophagous loops.
SELF-CONSUMING GENERATIVE MODELS
Consider a sequence of generative models (GEN,,, where each model approximates reference probability distribution P,, At each generation 1 E N, the model g' trains from scratch on the dataset D' (D', D)) containing both nł, real samples Dt. from P, and n', synthetic samples Dt from trained generative model(s). The first-generation model G trains only on real data: n. = 0, D = 0.
Definition. An autophagous generative process is sequence of distributions (EN) where each generative model G' is trained on data that includes samples from previous models (=))
Definition. Let -ist(..-) denote a distance metric on distributions. A MAD generative process is a sequence of distributions (G')EE such that Eldist(G', P.)) grows with t.
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Claim. Under mild conditions, autophagous generative process is MAD generative process.
Two critical aspects affect whether a sequence of generative models goes MAD: the balance of real and synthetic training data and how the generative models synthesize data. We study three realistic autophagous mechanisms, each of which includes synthetic data and potentially real data in a feedback loop (recall Section and Figure 3):
The fully synthetic loop: Each model G for 2 2 trains exclusively synthetic data sampled from models (GT);=1 from previous generations, i.e., D -
The synthetic augmentation loop: Each model g for I. 2 2 trains on a dataset D' = (Dr, D:):: fixed set of real data D, from P,, plus synthetic data D from previous generations' models.
The fresh data loop: Each model G' for I. 2 trains on a dataset D (Dr, D:):: fresh set of real data D.d drawn from Pr, plus synthetic data D from previous generations' models.
Metrics for MADness. Throughout this paper we measure the distance between the synthetic data and the real data (reference distribution) using the Fréchet inception distance (FID) (Heusel et al., 2017),* 4 the quality of the synthetic data using precision, and the diversity of the synthetic data using recall (Kynkäänniemi et al., 2019). See Appendix A.4 for more details.
2.1 BIASED SAMPLING IN AUTOPHAGOUS LOOPS
While the above three autophagous loops realistically mimic real-world generative model training scenarios that involve synthetic data, it is also critical to consider how each generation's 's synthetic data is produced in practice. In particular, most syntheses are to some degree biased to maximize perceptual quality, whether through manual curation "ccherrypiccking" or common techniques that automatically boost quality and sacrifice diversity by sampling closer to the modes of the synthetic distribution of the generative model (OpenAI, 2023; Ho and Salimans, 2021; Karras et al., 2020; Brock et al., 2019; Humayun et al., 2022). We refer to this common practice as sampling bias. We employ number of generative models in experiments below; each has unique controllable parameter to increase sample quality. We unify these parameters the universal sampling bias parameter À [0, 1], where À= = corresponds to unbiased sampling and À = O corresponds to sampling from the modes of the generative distribution G with zero variance. The exact interpretation of X differs across various models, but in general synthetic sample quality will increase and diversity will decrease as À is decreased from 1. Below we provide specific definitions for À for the various generative models we consider in this paper:
Gaussian models: To implement biased sampling from an estimated distribution W E), we sample from ((, XE). As decreases, we draw samples closer to the mean p4:
Generative adversarial networks: In our StyleGAN2 experiments, we decrease the truncation parameter [0, 1] to increase sample quality (Karras et al., 2020). Thus, >=
Diffusion models: For DDPMs, we use a classifier-fre free diffusion guidance factor w (with 10% conditioning dropout) (Ho and Salimans. 2021) and define
I+w'
3 THE FULLY SYNTHETIC LOOP: TRAINING EXCLUSIVELY ON SYNTHETIC DATA LEADS TO MADNESS
First, we analyze the fully synthetic loop, where each model trains on synthetic data from previous generations. We focus the inter-generational propagation of non-idcalities resulting from estimation errors and sampling biases and characterize the convergence of the autophagous loop. The fully synthetic loop's simplicity primarily reflects niche examples like training generative models their own high-quality outputs (followfox.a) ai, 2023). Nevertheless, this loop represents a worst-case scenario that provides insights into the more practical autophagous loops discussed in subsequent sections. Our analysis and experiments support our main conclusion for the fully synthetic loop: either the quality (precision) or the diversity (recall) of the synthetic data deteriorates over generations.
WWe calculate MNIST FIDs via LeNet (Lecun al., 1998) features instead of Inception features.
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Figure 4: Training generative models in a fully synthetic loop reduces both the quality and diversity of synthetic data, depending on sampling bias. We plot the FID, precision (quality), and recall (diversity) of the synthetic FFHQ and MNIST images from a fully synthetic loop with unbiased (A = 1) and biased (A < 1) StyleGAN2 and DDPM models. See Figure for StyleGAN2 samples demonstrating that the fully synthetic loop amplifies sample artifacts. In all cases, FID increases and diversity decreases. However, sampling bias can salvage quality (at the expense of diversity).
Gaussian fully synthetic loop: random walks and variance collapse. We first show that these loops have a martingale nature that causes MADness. Consider a reference distribution P, = NN Eo), where 140 Rd and Eg E Rdd and Gaussian generative process G = NW E.). At each
time t N, we sample n, vectors from gt with bias À S 1; i.e., we draw x ........ x ~ N( 11 From these vectors we construct the unbiased parameters of the next model g+:
lid
F4
Σ
[x] m.) - Mz)
T2.s
11g
It is straightforward to that f4, and E, (surer)martingale processes (Williams, 1991) that take random walks. For Σ,, we also have the following result that is proved in Appendix B. Proposition. For the random process defined in Equation (I), for any X S 1, we have E, a.s. O.
That is, when we repeatedly fit a distribution to data sampled from that distribution, we should not only expect some modal drift because of the random walk in μe (reduction in quality) but also inevitably a collapse of the variance E, (vanishing of diversity).
The key takeaway is that these effects-the the random walk and the variance collapse-ar are solely due to the estimation error of fitting the model parameters using random data. Importantly. this result holds true even when there is sampling bias (A 1). The magnitudes of the steps of the random walk in are determined by two main factors: the number of samples nt, and the covariance E. Unsurprisingly, the larger the ni the smaller the steps of the random walk, since there will be less estimation error. This will also slow the convergence of Σg to 0. Meanwhile, E, can be controlled using sampling bias factor X 1. The smaller the choice of A, the more rapidly E, will converge to 0, stopping the random walk of μ4: (as illustrated in Figure 15). Thus, the sampling bias factor provides a trade-off to preserve quality at the expense of diversity. Shumailov et (2023) recently showed that the expected Wasserstein-2 distributional distance IE E[dist(G', P.)] increases in this process, supporting our conclusion that G is a MAD generative process.
We now empirically study the fully synthetic loop using FFHQ-trained StyleGAN2 and MNIST- trained DDPM models; see Appendix A. for the experimental details.
Unbiased sampling degrades synthetic data quality and diversity. Figure 4 plots the FID, precision, and recall for SFFHQ-StyleGANY and MNIST-DDPM models fully synthetic loops with (A < 1) and without (A 1) sampling bias. In the latter case, the synthetic data distributions undergo random walks that deviate from the reference distribution because each generation's 's training data finite. Consequently, the models go MAD: FID increases, while precision and recall steadily decrease.
Biased sampling can boost synthetic data quality, but at the expense of diversity. As for the biased FFHQ-StyleGAN2 and MNIST-DDPM models (A 0.7 and 0.5) in fully synthetic loops
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Figure 5: Training generative models on biased synthetic data in a fully synthetic loop progres- sively loses diversity. We repeat the experiment from Figures and 4 but with sampling bias À = 0.7. The randomly selected syntheses clearly lose diversity. Appendix E displays additional samples.
A=
Generation t= = == 0.8 t= 10
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t 10
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Figure 6: In the fully synthetic loop, unbiased sampling loses quality, while biased sampling loses diversity. 2D UMAP projections of 784-dimensional MNIST-DDPM samples from fully synthetic loops without (left, 1) and with (right, X < 1) sampling bias. Without sampling bias, the synthetic digits become unrealistic (low-quality) that they are easily distinguishable from real digits, while with sampling bias, the digits remain realistic but progressively lose diversity, See Appendix F for the synthesized samples.
(see Figure 4), sampling bias increases precision but also accelerates losses in recall (shown clearly in Figure 5) compared to unbiased models. Moreover, the FID) still increases. indicating a MAD generative process. See Figure in Appendix C.3 for results with different MNIST-DDPM sampling bias values, which follow the same trend.
Synthetic mode behavior depends on the sampling bias. To visualize MAD generative processes, in Figure 6 we reduced the dimensionality of the real and synthetic MNIST-DDPM fully synthetic loop samples from Figure via Uniform Manifold Approximation and Projection (UMAP) (MeInnes al., 2018). With unbiased sampling, the ten modes of the synthetic distribution (one for each digit) progressively drift away from the real distribution modes, despite originating from a conditional model, and eventually merge into large cluster. By generation & 10. the synthetic digits illegible (Figure 24 in Appendix F). In sharp contrast to the unbiased case, UMAP reveals that biased sampling successfully keeps syntheses on the real data manifold (high precision), but contracts the synthetic support around a single set of ten digits (zero recall). Appendix C confirms these trends for Gaussian mixtures, WGANs, and Normalizing Flows.
4 THE SYNTHETIC AUGMENTATION LOOP: FIXED REAL TRAINING DATA CAN DELAY BUT NOT PREVENT MADNESS
While analysis of the fully synthetic loop is straightforward, practitioners will use real data when it is available. We now explore the synthetic augmentation loop, where a fixed real dataset augmented with autophagous synthetic data. Synthetic data augmentation can improve classification (Luzi et al., 2024; Burg et al., 2023), but the impact of autophagous data augmentation is unclear does increasing training data volume enhance synthesis, even if the added samples stray from reality? We find that, in the synthetic augmentation foop.fixed real training data only delays the inevitable degradation of the quality diversity of synthetic data over generations.

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Figure 7: Training generative models in synthetic augmentation loop without sampling bias reduces synthetic quality and diversity, albeit more slowly than in the fully synthetic loop. We plot the FIID, precision (quality), and recall (diversity) of FFHQ StHH--StyeGAA22 syntheses from synthetic augmentation loop, wherein generative models train on both synthetic and real data, and fully synthetic loop from Figure for comparison. Both loops have no sampling bias (A 1). Qualitative examples (Appendix G) show the same artifacts as in Figure 1, albeit less prominently.
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Figure 8: When incorporating real data in the synthetic augmentation loop, sampling bias still affects MADness. We plot the FID, precision (quality), and recall (diversity) of MNIST-DDPM images synthesized in synthetic augmentation loops with different sampling biases All three metrics exhibit the same, albeit less pronounced, behavior as in the biased fully synthetic loops depicted Figure 4.
Keeping the original real dataset the synthetic augmentation loop only slows MADness. Figure shows that keeping the full FFHQ dataset in StyleGAN2* synthetic augmentation loop still produces the same symptoms (albeit more slowly) as the fully synthetic loop: the distance from the real dataset (FID) increases, while the quality (precision) and diversity (recall) of synthetic samples still decrease without sampling bias. (See Appendix A.2 for the experimental details.) In fact, in Appendix bias À impacts MNIST-DDPM synthetic augmentation loops (Figure 8) in the same way it impacts fully synthetic loops: FID still increases, but can increase quality (precision) in exchange for diversity (recall). Additional synthetic augmentation loop experiments can be found in Appendix H.
see the same artifacts as in Figure and Appendix D. Additionally, sampling
5 THE FRESH DATA LOOP: FRESH REAL DATA CAN PREVENT MADNESS
Our most elaborate autophagous loop model obtains training data from two sources: unseen (fresh) real data and synthetic data from previously trained models. A clear instance of this the LAION-SB dataset (Schuhmann et al., 2022), which contains both real and Al-synthesized images from the Internet (Figure 2). We seek to understand how generative models evolve in the fresh data loop, which alters the synthetic augmentation loop by incorporating fresh (instead of fixed) real samples at
Unique to our StyleGAN2 synthetic augmentation loop, linearly grow pool of synthetic data assess whether access all previous generations' synthetic data could help future generations leam (see Appendix A.2).
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Figure 9: In a fresh data loop, generative models converge to a state independent of the initial generative model. We plot the Wasserstein distance (WD) and FID of two fresh data loop models: a Gaussian with nt = 100, nt = 900 (left) and an MNIST-DDPM with n, = n2 = 2000 (right). We simulate the former with both unbiased and biased sampling. Across all models, we see that the asymptotic WD and FID are independent of the initial real samples Nani and the initial WD or FID.
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Figure 10: In a fresh data loop, the admissible amount of synthetic data does not increase with the amount of real data. As the real data count n, increases, the synthetic data count n, for which ne 2 nrp (green area) converges. Synthetic data is only likely to be helpful for small ny.
each iteration. We imagine that a fraction p E (0, 1) of a corpus of data (c.g., the Internet) is real, and the remainder 1 p synthetic. Independently sampling n' data points from this corpus yields n² = pn' real and n = (1 p)n' synthetic data points to train the t-th generation model.
The fresh data loop reveals two intriguing phenomena. First, asymptotic performance converges independently of initial performance, depending only on the ratio of real-to-synthetic training data. Second, limited amounts of synthetic data can actually improve performance in the fresh data loop- since synthetic data propagates information from previously seen real data and thus increases the effective dataset size-but too much synthetic data can still cause MADness. Overall, our fresh data loop analyses and experiments establish that, with enough fresh real data, the quality and diversity of synthetic data do not degrade over generations.
Initial models will eventually be forgotten in the fresh data loop. First we show that the initial model does not affect the behavior of the fresh data loop. We train the initial model on n real samples and subsequent models with n, new real and n., synthetic (with bias X) samples from the previous model; see Appendix A.3 for the details. Interestingly, for both the Gaussian and MNIST- DDPM and models, the Wasserstein distance and FID converge independently of Rani after a few iterations (Figure 9). In other words, we observe that models in a fresh data loop converge to a limit point that depends ny, n,y and X, but not on the initial model G or its dataset size Nani.
lim E[dist(G' P+)] =: WD(n,, N). A). 100
(2)
For autophagy, this brings some hope: with fresh real data at each generation, Ejdist(g' PP)) does not necessarily increase with f. In other words, a fresh data loop does not necessarily go MAD.
The fresh data loop exhibits a phase transition. Since fresh real data mitigate MADness, one might suspect that synthetic data can provoke fresh data loop MADness. However, the truth that modest amounts of synthetic data in fresh data loops actually boost performance; only when the
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amount of synthetic data exceeds a critical threshold do models suffer. We formalize this observation through Monte-Carlo simulation of the fresh data loop limit point (Equation (2)) in Gaussian models. For comparison, we compute the effective sample size n. that alternative model would need to reach the same performance as the asymptote from scratch:
Find Re s.t. ((ddst((((n),, Pr)] WD(n,, ueg A).
That is, captures the asymptotic sample efficiency of the fresh data loop.
Figure 10 depicts how the ratio ne/n, changes with ny, Rgs and X. When ne/n, 2 1, we say the amount of synthetic data n, is admissible because it effectively increases the number of real samples. For n./n, < 1, synthetic data effectively reduces the number of real samples.
First, we confirm that, given The and À < 1, there exists phase transition in ni. If n, exceeds the admissibility threshold, then the effective sample size ne drops below the fresh sample size ny, meaning that synthetic data does not asymptotically improve performance. However, the synthetic-to- real ratio n,/nn needed to achieve ne/n, 2 1 is not constant. In fact, in Figure 10 we see that the admissible amount of synthetic data n, (such that na/n,, 2 1) can be quite high for small values of n,, but as n, grows, the admissible ratio of synthetic-to- to-rell data ng/nn, shrinks.
Second, we find that the admissible threshold value for n, depends strongly the sampling bias A. Perhaps surprisingly, stronger bias (smaller X) actually reduces the number of synthetic samples that can be used without harming performance. Taking the limit À + 1 for unbiased sampling appears to ensure that the effective number of samples is always increased (ne/n, n, is always greater than 1). Whether this limiting behavior extends beyond Gaussian models is an open question. As we discussed in Section 2.1, 1 it is unlikely that practical generative models synthesize without bias, and so it is better to draw conclusions from the case. See Appendix for additional fresh data loop experiments.
6 DISCUSSION
Our theoretical and empirical analyses have enabled to extrapolate what might happen as generative models become ubiquitous and train future models in autophagous (self-consuming) loops. Using state-of-the-are generative image models and datasets, we have studied three families of autophagous loops and identified the key rôle of sampling bias. Some ramifications are clear: without enough fresh real data, future generative models are doomed to Model Autophagy Disorder (MAD), progressively losing quality (precision) or diversity (recall) and amplifying generative artifacts. One doomsday scenario is that, if left uncontrolled, MAD could poison the entire Internet's 's data quality and diversity. After all, our autophagous loops went appreciably MAD after just 5 generations (Figure 1). It seems inevitable that AI autophagy's unintended consequences could arise in the near future.
Practitioners who deliberately use synthetic training data should heed our warning. For those in truly data-scarce applications, our results suggest how much real data can prevent MADness. For example, future training of medical image generator (DuMont Schütte et al., 2021) should ensure that all synthetic images are artifact-free and diverse (see Section 3), and that real (preferably new) data is maximally present in training (see Sections 4 and 5).
inter-institttions anonymous syntheses
Practitioners who unknowingly train on synthetic data could try controlling the ratio of real-to- synthetic training data by identifying and rejecting synthetic data. Some identifiers find telltale patterns of AI synthesis (Guarnera et al., 2020; Mitchell et al., 2023; Tang et al., 2023). Others make synthetic data steganographically idenfiable via watermarking (Kirchenbauer al., 2023a;b; Zhao et al., 2023; Peng et al., 2023; Wen et al., 2023; Fernandez et al., 2023; Fei et al., 2022). However, watermarking deliberately introduces hidden artifacts that could be uncontrollably or harmfully amplified by autophagy. In the fresh data loop, modest amounts of synthetic data can boost performance (m./n, > in Figure 10). Future research could develop autophagy-aware watermarking that helps identify synthetic data while avoiding the amplification of its own artifacts.
Future research directions include combining our three prototypical autophagous loops into more complex loops, examining how MADness affects downstream tasks (e.g., classification), and models for other data types. We have focused here on imagery, but autophagy and MADness can occur in any data type. For example, autophagous language models (Huang et al., 2022; Wang al., 2022; Taori et al., 2023) can also go MAD, losing quality (coherence or correctness) or diversity (variety). Shumailov al. (2023) have reached similar conclusions, but there is much work to do in this vein.

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ACKNOWLEDGEMENTS
Thanks to H. Javadi, B. Mason, and S. Sonkar for their insights. This work was supported by NSF grants CCF-191 1094, 1IS-1838177, and IIS-1730574; ONR grants N00014-18- 12-711,,,, N00014-20-1- 2534, and MURI N00014-20- 111-2200-127778 1-2787; AFOSR grant -99500-22-1-0060) DOE grant DE-SC0020345; and Vannevar Bush Faculty Fellowship. ONR grant N00014- 18-1-2047. DL was supported by ARO grant 2003514594.
REFERENCES
Tero Karras, Samuli Laine, and Timo Aila. A style-based generator architecture for generative adversarial networks. In CVPR, 2019a.
Tero Karras, Miika Aittala, Samuli Laine, Erik Härkönen, Janne Hellsten, Jaakko Lehtinen, and Timo Aila. Alias-free generative adversarial networks. In NeurIPS, 2021.
Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. High- resolution image synthesis with latent diffusion models. In CVPR, 2022.
OpenAl. GPT-4 technical report. arXiv preprint arXiv:2303.08771 2023.
Christoph Schuhmann et al. LAION-5B: An open large-scale dataset for training next generation image-text models. In NeurIPS Datasets and Benchmarks Track, 2022.
Matthew Gault. Al spam is already flooding the internet and it has an obvious tell. VICE, April 2023.
Matthew Cantor. Nearly 50 news websites are 'Al-generated", study says. Would be able to tell? The Guardian, May 2023.
Veniamin Veselovsky, Manoel Horta Ribeiro, and Robert West. Artificial artificial artificial intelli- gence: Crowd workers widely use large language models for text production tasks. arXiv preprint arXiv:23006.7060 07899, 2023.
Jon Christian. CNET secretly used on articles that didn't 't disclose that fact, staff say. Futurusm, January 2023.
Walter H. L. Pinaya, Detru-Daniel Tudosiu. Jessica Dafflon, Pedro Da Costa, Virginia Fernandez, Parashkev Nachev, Sebastien Ourselin, and M. Jorge Cardoso. Brain imaging generation with latent diffusion models. Deep Generative Models. Springer Nature, 2022.
Chengyuan Deng, Shihang Feng, Hanchen Wang, Xitong Zhang, Peng Jin, Yinan Feng, Qili Zeng, Yinpeng Chen, and Youzuo Lin. OpenFWI: Large-scale multi-structural benchmark datasets for full waveform inversion. In NeurIPS, 2022.
Lorenzo Luzi, Paul M Mayer, Josue Casco- Rodriguez, Ali Siahkoohi, and Richard G. Baraniuk. Boomerang: Local sampling on image manifolds using diffusion models. Transactions on Machine Learning Research, 2024.
Marvin Klemp, Kevin Rösch, Royden Wagner, Jannik Quehi, and Martin Lauer. LDFA: Latent diffusion face anonymization for self-driving applications. arXiv preprint arXiv:2302.08931, 2023.
Kai Packhäuser. Lukas Folle, Florian Thamm, and Andreas Maier. Generation of anonymous chest radiographs using latent diffusion models for training thoracic abnormality classification systems. arXiv preprini orXiv:22 1.01323, 2022.
August DuMont Schütte, Jürgen Hetzel, Sergios Gatidis, Tobias Hepp. Benedikt Dietz, Stefan Bauer, and Patrick Schwab. Overcoming barriers to data sharing with medical image generation: comprehensive evaluation. NPJ Digital Medicine, 2021.
Shekoofch Azizi, Simon Kornblith, Chitwan Saharia, Mohammad Norouzi, and David J Fleet. Synthetic data from diffusion models improves imagenet classification. arXiv preprint 2oXiv:2304008466 2023.
10

---

Published as a conference paper at ICLR 2024
Max F Burg, Florian Wenzel, Dominik Zietlow, Max Horn, Osama Makansi, Francesco Locatello, and Chris Russell. A data augmentation perspective on diffusion models and retrieval. arXiv preprint arXiv:2304.10253, 2023.
The Economist. The nigger-is-better approach to Al is running out of road. The Economist, June 2023a.
The Economist, Large, creative Al models will transform lives and labour markets. The Economist, April 2023b.
Pablo Villalobos, Jaime Sevilla, Lennart Heim, Tamay Besiroglu, Marius Hobbhahn, and Anson Ho. Will we run out of data? an analysis of the limits of scaling datasets in machine learning. arXiv preprint arXiv:2211.00 04325, 2022.
Ahmed Elgammal, Bingchen Liu, Mohamed Elhoseiny, and Marian Mazzone. CAN: Creative adversarial networks, generating "art" by learning about styles and deviating from style norms. arXiv preprini arXiv: 0e0. 2017.
Phillip Isola, Jun- Yan Zhu, Tinghui Zhou, and Alexei A Efros. Image-to-ing to-mage translation with conditional adversarial networks. In CVPR, 2017.
Aditya Ramesh, Mikhail Pavlov, Gabriel Goh, Scott Gray, Chelsea Voss, Alec Radford, Mark Chen, and Ilya Sutskever. Zero-shot text-to-image generation. ICML, 2021.
Tuomas Kynkäänniemi, Tero Karras, Samuli Laine, Jaakko Lehtinen, and Timo Aila. Improved precision and recall metric for assessing generative models. NeurlPS, 2019.
Jonathan Ho and Tim Salimans. Classifier-free diffusion guidance. In NeurlPS 2021 Workshop Deep Generative Models and Downstream Applications, 2021.
Natalie Jomini Stroud. Niche News: The Politics of News Choice. Oxford University Press, 2011.
Ivan Dylko, Igor Dolgov, William Hoffman, Nicholas Eckhart, Maria Molina, and Omar Aaziz. The dark side of technology: An experimental investigation of the influence of customizability technology on online political selective exposure. Computers in Human Behavior, 2017.
Michael A Beam. Automating the news: How personalized news recommender system design choices impact reception. Communication Research, 2014.
Eytan Bakshy, Solomon Messing, and Lada Adamic. Exposure to ideologically diverse news and opinion on Facebook. Science, 2015.
Derek O' O'Callaghan, Derek Greene, Maura Conway, Joe Carthy, and Pádraig Cunningham. Down the (white) rabbit hole: The extreme right and online recommender systems. Social Science Computer Review, 2015.
Neal Nathanson, John Wilesmith, and Christian Griot. Bovine Spongiform Encephalopathy (BSE): Causes and Consequences of a Common Source Epidemic. American Journal of Epidemiology. (55(11):559-965 06 1997. ISSN 0002-9262.
followfox.ai. The power of synthetic data: Infinite loop to improve fine-tuning results with sta- ble diffusion models, February 2023. URL https::/t/s/ttt Followfoxai. substack com/p/ data inattheeii--aatte-iiiiteeeee
Jiaxin Huang. Shixiang Shane Gu, Le Hou, Yuexin Wu, Xuezhi Wang, Hongkun Yu, and Jiawei Han. Large language models can self-improve. arXiv preprint arXiv:2210.116100 2022.
Tero Karras, Samuli Laine, Miika Aittala, Janne Hellsten, Jaakko Lehtinen, and Timo Aila. Analyzing and improving the image quality of StyleGAN. In CVPR, 2020.
Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. In NeurIPS. 2020.
Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C Courville. Improved training of Wasserstein GANs. NeurlPS, 201 7a.

---

Published as a conference paper at ICLR 2024
Ivan Kobyzev, Simon JD Prince, and Marcus A Brubaker. Normalizing flows: An introduction and review current methods. IEEE Transactions on Pattern Analysis and Machine Intelligence, 43 (11), 2020.
Tero Karras, Samuli Laine, and Timo Aila. style-based generator architecture for generative adversarial networks. In CVPR, 2019b.
Li Deng. The MNIST database of handwritten digit images for machine learning research [best of the web]. IEEE Signal Processing Magazine, 29(6), 2012.
Ilia Shumailov, Zakhar Shumaylov, Yiren Zhao, Yarin Gal, Nicolas Papernot, and Ross Ander- son. The curse of recursion: Training on generated data makes models forget. arXiv preprint arXiv:2305.17493, 2023.
Gonzalo Martínez, Lauren Watson, Pedro Reviriego, José Alberto Hernández, Marc Juarez, and Rik Sarkar. Combining generative artificial intelligence (AT) and the Internet: Heading towards evolution or degradation? arXiv preprini arXiv:2303.01255. 2023a.
Gonzalo Martínez, Lauren Watson, Pedro Reviriego, José Alberto Heránndez, Marc Juarez, and Rik Sarkar. Towards understanding the interplay of generative artificial intelligence and the Internet. arXiv preprint arXiv:2306.066 2023b.
Ryuichiro Hataya, Han Bao, and Hiromi Arai. Will large-scale generative models corrupt future datasets? arXiv preprint S.Xiv:2211.08099 2022.
Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. GANs trained by two time-scale update rule converge to local Nash equilibrium. In NeurIPS, 2017.
Y. Lecun, L. Bottou, Y. Bengio, and P. Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 1998.
Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale GAN training for high fidelity natural image synthesis. In ICLR, 2019.
Ahmed Imtiaz Humayun, Randall Balestricro, and Richard Baraniuk. Polarity sampling: Quality and diversity control of pre-trained generative networks via singular values. In CVPR, 2022.
David Williams. Probability With Martingales. Cambridge University Press, 1991.
Leland McInnes, John Healy, Nathaniel Saul, and Lukas Grossberger. UMAP: Uniform manifold approximation and projection. The Journal of Open Source Software, 3(29):861, 2018.
Luca Guarnera, Oliver Giudice, and Sebastiano Battiato. Deepfake detection by analyzing convolu- tional traces. In CVPR workshops, 2020.
Eric Mitchell, Yoonho Lee, Alexander Khazatsky, Christopher D Manning, and Chelsea Finn. De- machine-generated
tectGPT: Zero-shot machine- generated text detection using probability curvature. In Proceedings of the 40th International Conference on Machine Learning, volume 202, pages 24950-24962 2023.
Ruixiang Tang, Yu-Neng Chuang, and Xia Hu. The science of detecting L.M -.ne-aeeedtedd texts. arXiv preprint arXiv:2303.077 0070000 2023.
John Kirchenbauer. Jonas Geiping, Yuxin Wen, Manli Shu, Khalid Saifullah, Kezhi Kong, Kasun Fernando, Aniruddha Saha, Micah Goldblum, and Tom Goldstein. On the reliability of watermarks for large language models. arXiv preprint arXiv:2306.0466 2023a.
John Kirchenbauer, Jonas Geiping, Yuxin Wen, Jonathan Katz, Ian Miers, and Tom Goldstein. A watermark for large language models. arXiv preprint vrXiv:2301.10226. 2023b.
Yunqing Zhao, Tianyu Pang, Chao Du Xiao Yang, Ngai-Man Cheung, and Min Lin. A recipe for watermarking diffusion models. arXiv preprint arXiv:2303. 2023.
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Sen Peng, Yufei Chen, Cong Wang, and Xiaohua Jia. Protecting the intellectual property of diffusion models by the watermark diffusion process. arXiv preprint arXiv:2306.034366 2023.
Yuxin Wen, John Kirchenbauer, Jonas Geiping, and Tom Goldstein. Tree-ring watermarks: Fin- gerprints for diffusion images that are invisible and robust. arXiv preprint arXiv:2305.20030, 2023.
Pierre Fernandez, Guillaume Couairon, Hervé Jégou, Matthijs Douze, and Teddy Furon. The stable signature: Rooting watermarks in latent diffusion models. arXiv preprint urXiv:2303.1544 2023.
Jianwei Fei, Zhihua Xia, Benedetta Tondi, and Mauro Barni. Supervised GAN watermarking for intellectual property protection. In Workshop on Information Forensics and Security (WIFS), 2022.
Yizhong Wang, Yeganeh Kordi, Swaroop Mishra, Alisa Liu, Noah A Smith, Daniel Khashabi, and Hannanch Hajishirzi. Self-instruct: Aligning language model with self generated instructions. arXiv preprint 2rXiv:2222.00666 2022.
Rohan Taori, Ishaan Gulrajani, Tianyi Zhang, Yann Dubois, Xuechen Li, Carlos Guestrin, Percy Liang, and Tatsunori B Hashimoto. Alpaca: A strong, replicable instroction-follovinng model, 2023.
Leonid Kantorovich. Mathematical methods of organizing and planning production. Management Science, 6(4), 1960.
Tong Che, Ruixiang Zhang, Jascha Sohl-Dickstein, Hugo Larochelle, Liam Paull, Yuan Cao, and Yoshua Bengio. Your GAN is secretly an energy-based model and you should use discriminator driven latent sampling. NeurIPS, 2020.
Laurent Dinh, Jascha Sohl-Dickstein, and Samy Bengio. Density estimation using Real NVP, In International Conference Learning Representations, ICLR, 2016.
Durk P Kingma and Prafulla Dhariwal. Glow: Generative flow with invertible 1 convolutions. In Advances in Neural Information Processing Systems, 2018.
Filippo Pagani, Martin Wiegand, and Saralees Nadarajah. An n-dimensional Rosenbrock distribution for Markov chain Monte Carlo testing. Scandinavian Journal of Statistics, 49(2), 2022.
Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron Courville. Improved training of Wasserstein GANs. In Advances in Neural Information Processing Systems, 2017b.
Rafael Orozco, Philipp Witte, Mathias Louboutin, Ali Siahkoohi, Gabrio Rizzuti, Bas Peters, and Felix J. Hermann. invertibleNetworks.il A Julia package for scalable normalizing flows. Preprint arXiv:23/2.13440, 2023.
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A EXPERIMENT SETUPS
Here are detailed descriptions of our experiments.
A. THE FULLY SYNTHETIC LOOP
We empirically study the fully synthetic loop using two representative deep generative models and two practical training datasets. After training an initial model g' with a fully real dataset containing n. samples from the (unknown) reference distribution, subsequent models (g are trained using n", synthetic samples from the immediately preceding model gt-1, where each synthetic sample is produced with sampling bias A. Our primary experiments are organized as follows:
Generative adversarial network: We use an unconditional StyleGAN2 model (Karras et al., 2020) and initially train it on n 70k samples from the FFHQ dataset (Karras et al., 2019b). We downsized the FFHQ images to 128 x 128 (using Lanczos PyTorch anti-aliasing filtering as in Karras et al. (2020)) to reduce the computational cost. We set n² = 70k for 2 2.
Diffusion model: We use conditional DDPM (Ho al., 2020) with T = 500 diffusion time steps and initially train it on n, = 60k real samples from the MNIST dataset. We set n = 60k for 2 2. To calculate FIDs, we use the features extracted by LeNet (Lecun et al., 1998) rather than an Inception network, because numerical digits are not exactly natural images. For consistency, we continue use the term "FID" in this case.
A.2 THE SYNTHETIC AUGMENTATION LOOP
We simulate the synthetic augmentation loop using the same deep generative models and experimental conditions as Appendix 1. Recall that we first require training an initial model G' with a fully real dataset of n samples. All subsequent models (G))E= are trained using n., synthetic samples from the previous model(s) and all of the original n. samples used to train G Note that each synthetic sample is always produced with sampling bias X. Our experiments organized follows:
Generative adversarial network: We use an unconditional StyleGAN2 architecture Karras et al. (2020) trained the FFHQ-128 128 dataset Karras al. (2019b). Like the StyleGAN experiment in Appendix 1, at each generation 2 2 we sample 70k images with no sampling bias (A 1) from the immediately preceding model Gt However, now the synthetic dataset D' includes samples from all the previously models (GT)(=) producing a synthetic data pool of size n², = (t 1)70k that grows linearly with respect
The real FFHQ dataset always
present at every generation: D = D; and n n² = 70k for every generation t.
Diffusion model: We use conditional MNIST-DDPM Ho et al. (2020) with T = 500 diffusion time steps. In this experiment the synthetic dataset D is only sampled from the previous generation g'-l with sampling bias X, and n,. = n = 60k for all t 2 2. The original real MNIST dataset is also available at every generation: D. DJ and n. n 60k for all t.
A.3 THE FRESII DATA LOOP
As in previous autophagous loop variants, we assume that all models are initially trained solely on real samples, with the number of real samples denoted here as nit = Mini. In subsequent generations (i.e., for 2 2) the generative models are trained with a fixed number of real samples, denoted as n² = n2., and fixed number of synthetic samples, denoted by n', = ng. In the fresh data loop, the dataset D' is independently sampled from the reference probability distribution P,, while the dataset D is sampled exclusively from the previous generation Gr-1, with sampling bias represented as
We simulate the fresh data loop using different values for Nimis nly Ns, and X. The Gaussian example enables examination of the fresh data loop in greater detail, especially in the asymptotic regime, Meanwhile, our MNIST-DDPM example demonstrates the impact of fresh data loop on more realistic dataset and model.
Gaussian model: We consider normal reference distribution P, ~N(Os, Ia) with dimension 100. For modeling the Gaussian distribution, we utilize an unbiased moment estimation approach, as described in Equation (1).
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Diffusion model: We use conditional DDPM Ho al. (2020) with T 500 diffusion time steps. We consider the MNIST dataset as our reference distribution.
A.4 METRICS FOR MADNESS
Ascertaining whether an autophagous loop has gone MAD or not (recall Definition 2) requires that measure how far the synthesized data distribution g" has drifted from the true data distribution P, over the generations t. We use the notion of the Wasserstein distance as implemented by the Fréchet Inception Distance (FID) for this purpose. We will also find the standard concepts of precision and recall useful for making rigorous the notions of quality and diversity, respectively.
Wasserstein distance, earth mover's or optimal transport distance (Kantorovich, 1960), measures the minimum work required to move the probability mass of one distribution to another. Computing the Wasserstein distance between two datasets (e.g., real and synthetic images) prohibitively expensive. As such, standard practice employs the FID (Heusel et al., 2017) as an approximation, which calculates the Wasserstein-2 2 distance between Inception feature distributions of real and synthetic images. For our MNIST experiments we calculate FIDs using the features from LeNet (Lecun et al., 1998) rather than an Inception network, because numerical digits are not exactly natural images.
Precision quantifies the portion of synthesized samples that are deemed high quality or visually appealing. We use precision indicator of sample quality. We compute precision by calculating the fraction of synthetic samples that are closer to a real data example than to their k-th nearest neighbor (Kynkäänniemi al., 2019). We use the default & = 5 in all experiments.
Recall estimates the fraction of samples in a reference distribution that are inside the support of the distribution learned by generative model. High recall scores suggest that the generative model captures a large portion of diverse samples from the reference distribution. We compute recall in manner similar to precision (Kynkäänniemi et al., 2019). Given set of synthetic samples from the generative model, we calculate the fraction of real data samples that are closer to any synthetic sample than its k-th nearest neighbor. In Appendix C.I we demonstrate how recall captures synthetic diversity in an autophagous loop more accurately than variance.
B PROOF OF SYNTHETIC GAUSSIAN MARTINGALE VARIANCE COLLAPSE
We now prove that for the process described in Equation (I), E. a.a. O.
Proof. First write xi- = V + p for zi ~ ~NO0,, Ia). Then consider the process tr [Er].
which is lower bounded submartingale:
tr[E.] = Atr
1/2
N-1
N
1
(ad-m))(t) (z)(z) ut)T
Σ 1/2 1
(4)
where 1n = = M4 z By Doob's martingale convergence theorem (Williams, 1991, Ch. 11), there exists a random variable wr such that tr[E.] -h", w, and now show that we must have w Without loss of generality, we can assume that Σ, is diagonal, in which case it becomes clear that tr|E,] a generalized x² random variable, being linear combination of independent x² random variables with N - degrees of freedom, mixed with weights Adiag( E,-1) Therefore, we can write tr[E.] = ty (y,tr(E,11) where y/ is generalized x2 random variable with the same degrees of freedom but with mixing weights diag E,-1)/tr ////////r,,/,,//// and E(ya E,-1]
1. This implies that at least one mixing weight is greater than 1/D for each f, which means that for any 0 < < 1, there exists > 0 such that Pr( infinitely often with probability one, the only w that satisfy lim,- tr tr| IT. V.
e) c. Now consider the case X = 1. Since 13: 1
is W. = O. For general & 1, tr Σ,] is simply the product of the process for À = and the sequence 1-1 and so the product must also converge to zero almost surely. Finally, since tr [r] a.s. 0. we also must have E, a.s. O, where convergence is defined with any matrix norm.
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C ADDITIONAL EXPERIMENTS FOR THE FULLY SYNTHETIC LOOP
Here we present additional experiments for the fully synthetic loop.
C.I RECALL VERSUS VARIANCE: GMMS IN AN UNBIASED FULLY SYNTHETIC LOOP
We also trained 2D GMMs in an unbiased fully synthetic loop using the same 25- 2o-mode distribution as (Che et al., 2020). Figure we see that the fully synthetic loop gradually reduces the number of modes covered by the synthetic distribution. Various metrics could measure this loss in diversity, so Figure 12 we explore how well each metric reflects the dynamics of the fully synthetic loop, finding that recall is best-equipped to measure diversity in multimodal datasets.
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Figure 11: The fully synthetic loop gradually causes mode collapse. Estimated GMM (Che et al., 2020) distributions after 1, 200, and 2k iterations of unbiased fully synthetic loop. Notice that the modes are lost asymptotically.
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Figure 12: Recall the most suitable commonly accepted metric for diversity in an autophagous loop. For GMMs in a fully synthetic loop (Figure 11), there are three primary potential metrics of diversity: variance,' 7 average modal variance (the average variance of each mode), and recall (Kynkäänniemi al., 2019). We observe that the overall variance (left) does not reflect the loss of modes that we see Figure as smoothly as recall (right) and average modal variance (middle). Recall is therefore suitable choice for measuring diversity in multimodal datasets and, unlike average modal variance, is compatible with distributions where the number modes is not tractable (e.g., natural images).
C.2 WASSERSTEIN GANS IN AN UNBIASED FULLY SYNTHETIC LOOP
In this experiment we trained Wasserstein GANs (with gradient penalty) (Guirajani et al., 2017a) on the MNIST dataset fully synthetic loop for 100 generations. As shown Figure 13, the FID monotonically increases, while quality (precision) and diversity (recall) monotonically decrease.
For multidimensional datasets, calculate variance the of covariance.
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0.3
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Figure 13: The negative effects of the fully synthetic loop are monotonic and inescapable. The FID (left), quality (precision, middle), and diversity (recall, right) of synthetic FFHQ and MNIST images produced by MNIST Wasserstein GANs.
C.3 ADDITIONAL MNIST-DDPM FULLY SYNTHETIC LOOP RESULTS
In Figure we showcased the results of training MNIST-DDPMs fully synthetic loop with various sampling bias factors X. In Figure 14 we have the results (FID, precision, and recall) more generations and different sampling biases X.
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DDPMs an MNIST fully synthetic loop:
D.66
fully synthetic loop, sampling bias can mitigate distributional drift and losses in quality, but only at the cost of rapid losses in diversity The FID (left), quality (precision, middle), and diversity (recall, right) of synthetic images from an MNIST-DDPM fully synthetic loop.
Figure 14:
C.4 NORMALIZING FLOW FULLY SYNTHETIC LOOP
We implemented the fully synthetic loop using normalizing flows (Dinh et al., 2016; Kingma and Dhariwal, 2018) for generative modeling of the two-dimensional Rosenbrock reference distribution (Pagani et al., 2022) in order to visualize the outcome of this particular scenario in a controlled setting. Normalizing flows are unique in that they enable exact evaluation of the likelihood of the estimated distribution due to their invertibility (Dinh et al., 2016). This leads relatively straightforward training procedure compared GANs, which often require careful balancing between the generator and discriminator networks avoid mode collapse (Gulrajani et al., 2017b). Therefore, by using a low-dimensional reference distribution, this setup allows us to demonstrate the fully synthetic loop while eliminating potential training imperfections. We implemented this example using the InveribleeNtwwors.]] (Orozco et al., 2023) package for normalizing flows.
According the fully synthetic loop setup, we start with training dataset of 10 samples from the 2D Rosenbrock distribution with the density function (, x22) x exp 1-12 (z2 - ==?²²
(Pagani et al., 2022), which is plotted on the left-hand side of Figure 15. The subsequent generations of normalizing flow models are trained using synthetic data generated by the previous pre-trained normalizing flow for 16 generations, both with and without sampling bias. We employ the GLOW normalizing flow architecture (Kingma and Dhariwal, 2018) with eight coupling layers (Kingma and Dhariwal, 2018) and hidden dimension of 64. The training is carried out for 20 epochs with batch size of 256 for each generation, ensuring convergence as determined by monitoring the
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model's likelihood over validation set. Figure 15 summarizes the results of this fully synthetic loop setup. To incorporate sampling bias, we sample from (O,, ATa) from the latent space of the model, where d = 2. As shown, regardless of the presence of sampling bias, the resulting distribution after 16 generations loses the tails of the reference distribution, indicating loss of diversity. This phenomenon becomes more pronounced when sampling bias is present (A < 1).
1=1
16
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Ground Truth
1=1
A=0.75
0-0.75
Figure 15: Normalizing flows are not immune to the fully synthetic loop. The fully synthetic loop implememted with formalizing flow (Dinh al., 2016) applied to the 2D Rosenbrock distribution (Pagani et al., 2022). Sampling with or without bias still loses the tails of the distribution (i.c., diversity). Using A < 1 accelerates this loss of diversity.
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D FFHQ UNBIASED FULLY SYNTHETIC LOOP IMAGES
We show additional randomly chosen synthetic samples produced by the same FFHO-StyleGAN2 unbiased fully synthetic loop in Figure I.
Figure 16: Generation of fully synthetic loop with bias X 1. i... synthetic samples from the first model g¹.
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Figure 17: Generation fully synthetic loop with bias À
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Figure 18: Generation of fully synthetic loop with bias À
Figure 19: Generation of fully synthetic loop with bias À
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D
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Figure 20: Generation of fully synthetic loop with bias À
E FFHQ BIASED FULLY SYNTHETIC LOOP IMAGES
We show additional randomly chosen synthetic samples produced by the same FFHQ-StyleGAN2 for biased (A = 0.7) fully synthetic loop as in Figure
Figure 21: Generation of a fully synthetic loop with bias À = 0.7
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Figure 22: Generation of a fully synthetic loop with bias X 0.7
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Figure 23: Generation of a fully synthetic loop with bias X 0.7
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F MNIST-DDPM FULLY SYNTHETIC LOOP IMAGES
Here we show randomly chosen samples from each generation of an MNIST-DDPM in fully synthetic loop for different sampling biases.
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Figure 24: Without sampling bias, synthetic data modes drift from real modes and merge
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Figure 25: With sampling bias, synthetic data modes drift and contract around just few high-quality data points. Randomly selected synthetic MNIST images of each generation without sampling bias (A = 0.8). See Figure 6 for more details.
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G FFHQ UNBIASED SYNTHETIC AUGMENTATION LOOP IMAGES
Figure 26: Generation / of synthetic augmentation loop with bias X See Figure 16 for the samples from t = (in any autophagous loop the first model G' always trains on purely real data, see Section
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Figure 27: Generation / 6 of synthetic augmentation loop with bias À - 1
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H ADDITIONAL RESULTS FOR THE SYNTHETIC AUGMENTATION LOOP
H.1 THE MNIST-DDPM SYNTHETIC AUGMENTATION LOOP
In this section, repeat the experiment in Fig and described in A.2 using all synthetic data from previous generations, i.e, at each iteration & we used n = ( 1)6kk synthetic samples from (f=) combined with the initial real data we had. The results are shown in Figure 28. We see the same trend as Figure 8. For better comparison between using synthetic samples from all previous generations only using from the previous generation is shown in Figure 29, Using synthetic data from all previous generations only slows down the process the degradation models with respect to only using data from previous generations.
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Figure 28:
Using samples from all previous generative models in synthetic augmentation loop will not stop MA MADness. We show the FID, precision (quality), and recall (diversity) of MNIST- DDPM images synthesized in synthetic augmentation loops with different sampling biases X. All three metrics exhibit the same behavior in the case we only sample from the previous generation shown in Figure 8.
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Figure 29: Using samples from all previous generative models in synthetic augmentation loop slows the degradation of models more. We show the FID of MNIST-DDPM images synthesized in synthetic augmentation loops with different sampling biases À using synthetic data from all previous generation and only the last generation.
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Published as a conference paper at ICLR 2024
H.2 THE GAUSSIAN SYNTHETIC AUGMENNATION LOOP
In this section, we replicate the Gaussian experiment in Section 5 for synthetic augmentation loops.
In particular, we sample n, real data from the reference distribution P, =Oa0,,, [a) with dimension of = 100 to train the first model G For the next generations, we sample vıs synthetic data from model G with sampling bias and combine it with the same n,, real samples used to train G'. We report with n. defined in Equation 3.
We report the results for this experiment in Figure 30 and 31. We observe that for any values of n, d with d 100, the presence of synthetic samples reduces effective number of samples progressively. However, when the problem ill-posed, i.e. ny < d, Th can be increased with respect n, if some sampling bias is present in the system. However, in our experiments we observe that ne cannot surpass for any values of À or ne2 as it will always corresponds to an ill-posed problem ne < d.
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Figure 30: In a synthetic augmentation loop, we always see a decrease in ne with respect to except for very small values of n, 100, where the distribution estimation problem in ill-posed.
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Figure 31: In a synthetic augmentation loop, we always see decrease in with respect to Smaller values of result faster decay of n, as n, increases.
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I ADDITIONAL RESULTS FOR THE FRESH DATA LOOP
Here we provide three additional Gaussian experiments investigating the convergence of the fresh data loop.
Experiment 1: In Figure 10 we showed how Gaussian fresh data loop convergence depends and n, for few different values of Now we depict how convergence depends on ni, and for few different values of n,,.
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Figure 32: In a fresh data loop, sampling bias reduces the admissible synthetic sample size. For strong sampling bias (small A), the maximum synthetic data count n, for which ne 2 n, (green area) decreases.
In Section we assumed that we only sample from the previous generation g for creating the synthetic dataset Dr. In this experiment (G") Here n,, 103, n, 10 and X 1. In Figure 33 see how a. varies with respect to K. Increasing the memory K in sampling from previous generations can boost performance, however the rate of improvement becomes slower as increases. However the rate of improvement on ne sublinear with respect to K.
Experiment 2:
sample randomly from K previous models
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Figure 33: The effective sample size n. divided by the real sample size n, for different numbers of accessed previous generations K.
Experiment 3: Here we assume that we are sampling from an environment where percent of data
real, and the rest synthetic data from the previous generation G with sampling bias We change the total number of data in the dataset show the Wasserstein distance for different p and in Figure 34.
[D'|, with n, p and n. = =1 (1-n) x p. We
Let us first examine the dynamics of the Gaussian fresh data loop without sampling bias (A 1). We observe in Figure 34 (left) that the Wasserstein distance (WD) decreases with respect to dataset size However, the presence of synthetic data (p 100%) decreases the rate at which the WD decreases, and increases the overall WD each generation the fresh data loop. This means that with presence of synthetic data in the Internet, the progress of generative models will become slower
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Published as a conference paper at ICLR 2024
In the presence of sampling bias (A 1, Figure 34 right), that for close values of À to 1, the Wasserstein distance follows a sub-linear trend, meaning that eventually the rate of progress in generative models will effectively stop, matter how much (realistically) the total dataset size is increased.
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Figure 34: The Wasserstein distance (WD) versus the whole dataset size for different values of (left) and sampling bias (right).
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Reviews:
[{"review_id": "S0nkol1Tv5", "reviewer": "Reviewer_VGNe", "summary": "This paper investigates performance degradation of generative models in self-consuming (or autophagous) loops. The paper categorizes three scenarios of self-consuming based on real-world applications. In particular, a new scenario called \"fresh data loop\" is considered for the first time, where new data comes into the self-consuming loop. The empirical investigation on the scenarios reveals that, while the self-conuming loop tends to couse the degradation of the generative models, we can avoid it if the generative models in the loop continues to be exposed to new data. Also, the paper investigates how sampling techniques for better generation affects the degradation in the loop. It is empirically confirmed that these findings hold for different generative models or datasets.", "questions": "See Weaknesses.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The paper is clearly written and easy to follow. Their problem is appropriately formulated in a mathematically sound way.\n- In Section3, a toy example of gaussian models is analyzed, which provides a theoretical evidence for their heuristic Claim in Section 2.\n- It is predictable but also insightful that the performance degradation in the loop is caused only when using fixed samples over the loop.", "weaknesses": "- It is unclear what Claim in Section 2 aims for. Although it is proved for a toy model of gaussians, I assume that it is aimed for a hypothesis for general case but the authors seem not to explain such aspects. For example, is random walkness in Claim observed for practical models? If not, the claim would be overclaimed and somewhat doubtful for general case. Finally note that \"Claim\" in a paper is usually considerred as to be proven in the paper, not a hypothesis.\n- Eq. (2) is totally unclear. Is it a hypothesis or theorem? Where is $WD(n_r, n_s, \\lambda)$ defined? If it is just a hypothesis, the author should make it clear in the text.\n- It is unclear why $n_{ini}$ is considered in the first part of Section 5. How does it relate to the main claims in Introduction?\n- The observation of a phase transition is interesting, but it suddenly appears at Section 5. I recommend to briefly discuss the motivation and the results in Introduction.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "wYu5ELBfUM", "reviewer": "Reviewer_ZeQh", "summary": "This paper investigates the effect of repetition of the process that generated data of a generative model are included in the training data of generative models of next generation (self-consuming loop).\nThey categorize possible scenarios to 1. training data are fully generated, 2. training data are partially generated and real data are fixed, and 3. training data are partially generated and real data change.\nTheoretical and empirical analyses reveal that scenarios 1 and 2 lead generative models to collapse after some iterations of the loop.", "questions": "* To my understand, Huang et al. 2022 (cited in p3) considers \"synthetic data augmentation\", but Hataya et al. 2022 (cited in p3) focuses on the effects of the first loop of synthetic augmentation loops or fully synthetic loops on some downstream tasks, such as classification. Do I misunderstand something?\n* Why the authors choose StyleGAN2 with FFHQ and DDPM with MNIST?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "The topic, self-consuming loop, is relevant to the community, as generative models are more and more common and a plenty of generated data are released to the internet. This paper assumes three possible scenarios of the loop and analyzes each of them, which distinguishes this work.\nIt is also important that the authors discuss how to alleviate the effect of \"MAD\".", "weaknesses": "Although the authors define the autophagous mechanisms such that \"each generative model $\\mathcal{G}^t$ is trained on data that includes samples from previous models\" (p3), but to my understand, the theory (around eq 1) and the experiments (described in A.1 and A.2 diffusion model) only consider the case that each model $\\mathcal{G}^t$ is trained on data generated by $\\mathcal{G}^{t-1}$. \nThe discrepancy between the definition of autophagous mechanisms and the theory and experiments is worth noting otherwise it diminishes the soundness.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "xlBIHlsufl", "reviewer": "Reviewer_uRXW", "summary": "The work investigates autophagous generative processes, where generative models train on data that includes samples from AI-synthesized data, and identifies a phenomenon termed Model Autophagy Disorder (MAD). MAD refers to the progressive deterioration of both quality and diversity in synthetic data over generations. The presence of sampling bias, common in generative model training, influences the impact of MAD. This paper shows that with enough fresh real data, the quality and diversity of the generative models do not degrade over generations. Additionally, the paper reveals a phase transition in the admissibility of synthetic data in fresh data loops, with excessive synthetic data potentially leading to MADness.  This work also discusses that autophagous loop behaviors hold across a wide range of generative models and datasets.", "questions": "(1) Could the authors provide more insights into potential strategies or mitigations for addressing MAD in generative model training?\n\n(2) How might MAD impact domains beyond image generation, such as NLP or audio synthesis? Can the authors hypothesize on potential challenges and solutions in these areas?\n\n(3) The paper discusses the impact of sampling bias (λ). Could the authors provide a more nuanced analysis of how varying levels of sampling bias affect MAD, particularly in terms of quality and diversity?\n\n(4) Could the authors elaborate more on the mathematical foundations of MAD and its implications?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "(1) This paper identifies and addresses a novel issue in the field of generative modeling, the phenomenon of Model Autophagy Disorder (MAD) resulting from autophagous generative processes. This issue, which has not been extensively explored before, carries potential consequences for data quality and diversity in AI systems\n\n(2) The paper exhibits a well-structured and easily understandable presentation. It offers clear definitions, explanations, and visualizations to elucidate the concept.\n\n(3) The study conducts extensive experiments to probe autophagous generative processes across diverse scenarios, encompassing fully synthetic loops, synthetic augmentation loops, and fresh data loops. The inclusion of various generative models, approaches, and datasets enhances the robustness of the findings.\n\n(4) The paper's findings hold practical implications for the training of generative models, especially in situations involving synthetic data. They offer valuable insights and guidance for future model training endeavors.", "weaknesses": "(1) This work would benefit from a dedicated section discussing potential solutions or mitigations for Model Autophagy Disorder (MAD) in the training of generative models. This could enhance the paper's practical utility in the field.\n\n(2) A more in-depth exploration of the broader implications of MAD is expected.  This could involve exploring the impact of MAD in various domains beyond image generation, such as NLP or audio synthesis. Additionally, discussing real-world scenarios and applications where MAD could manifest would make the paper more informative.\n\n(3) To enhance the rigor of the paper, a more comprehensive theoretical framework should be developed to formalize the concept of MAD and its implications. A deeper exploration of the mathematical foundations underlying MAD would contribute to a stronger theoretical basis for the research.\n\n(4) The work lacks a detailed description of the sources or methods used to generate the synthetic data used in this study. Providing specifics on how synthetic data was created for experiments would enhance transparency and reproducibility.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (poster)