A Markovian View of Iterative-Feedback Loops in Image Generative Models: Neural Resonance and Model Collapse
Authors: Vibhas Kumar Vats, David J. Crandall, Samuel Goree
Organizations: Luddy School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN, USA · Department of Computer Science, Stonehill College, Easton, MA, USA
AI training datasets will inevitably contain AI-generated examples, leading to ``feedback'' in which the output of one model impacts the training of another. It is known that such iterative feedback can lead to model collapse, yet the mechanisms underlying this degeneration remain poorly understood. Here we show that a broad class of feedback processes converges to a low-dimensional invariant structure in latent space, a phenomenon we call neural resonance. By modeling iterative feedback as a Markov Chain, we show that two conditions are needed for this resonance to occur: ergodicity of the feedback process and directional contraction of the latent representation. By studying diffusion models on MNIST and ImageNet, as well as CycleGAN and an audio feedback experiment, we map how local and global manifold geometry evolve, and we introduce an eight-pattern taxonomy of collapse behaviors. Neural resonance provides a unified explanation for long-term degenerate behavior in generative models and provides practical diagnostics for identifying, characterizing, and eventually mitigating collapse.
Figures & tables
Figure 1: A high-level representation of the Iterative feedback process. (a) A graphical representation of the generational Markov chain and cartoon overview of our iterative generation settings. Xn represents the current distribution of images at generation n . (b) Data distribution distances for two experiments in scenario (3), and three experiments in scenario (4), measured using FID score. The top plot shows single-step changes between consecutive generations, while the bottom plot shows cumulative change from the original distribution. Experimental runs with differing numbers of generations are scaled to the width of the graph, so that the x-axis represents fraction of total generations, and each point is one generation.
Manifold Behavior
Local Metrics
Global Metric
Dimensional Pattern
Local
Global
σintra
mLB
PRG
Semantic Expansion Regime
Expansion
Expansion
↑
↑
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Coherent Expansion (CE)
Expansion
Contraction
↑
↑
↓
Wrinkled Expansion (WE)
Expansion
Expansion
↑
↓
↑
Anisotropic Expansion (AE)
Expansion
Contraction
↑
↓
↓
Oblate Expansion (OE)
Table 1: Latent - manifold dynamics under neural resonance. Each row lists a distinct combination of directional change in the local spread ( σintra ), the local curvature measure ( mLB ), and the global participation ratio ( PRG ). Patterns are grouped into two regimes, semantic expansion ( σintra↑ ) and semantic contraction ( σintra↓ ), and each is labeled according to its geometric character (e.g., coherent expansion, wrinkled contraction). An animation illustrating these patterns is provided in the Supplementary Video.
Table 2: Summary of observed latent manifold dynamics with sparkline plots. The dynamics is indicated with Coherent Expansion (CE), Wrinkled Expansion (WE), Oblate Expansion (OE), Coherent Contraction (CC), and Wrinkled Contraction (WC). LGR and LF means label-guided retrained and latent-feedback models, respectively. CyclaGAN experiment uses Horse-Zebra data. See Supplementary Materials for full plots with axes.
Figure 2: Evolution of class exemplars under iterative feedback. Columns: same-generation samples. (a–c) MNIST: latent-feedback progressively loses semantic coherence; label-guided and unconditional retraining retain class identity but converge to repetitive templates owing to high compressibility. (d–e) ImageNet-5: both regimes collapse, but differently: latent-feedback preserves coarse class cues while producing entangled objects; label-guided retraining loses most class semantics. (f) CycleGAN (non-ergodic): trajectories settle into distinct attractor basins between the two domains. Random examples from the same class are shown for each scenario.
Appendix figures & tables10 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 3: A idealized example of local and cumulative drifts in generational Markov chains. The blue curve ( FIDn,n−1 ) shows local drift between successive generations, and the orange curve ( FIDn,0 ) shows cumulative drift from the original data. When both curves have steep slopes, the chain is in an active transient phase; when one curve flattens and the other changes slowly, it is in a slow transient phase; and when both plateau, the system has reached empirical stationarity.
Figure 4: A high-level representation of the Iterative feedback process. Xn represents the current distribution of images at generation n and T(⋅) is the transformation operator. The framework unifies five feedback settings—Lucier’s acoustic experiment, cyclic image translation (CycleGAN), latent-feedback diffusion, and two retrained diffusion models (label-guided and unconditional)—each representing a distinct form of iterative feedback. Together they illustrate how successive generations of models form a Markov process and their shared dynamics.
Figure 5: Local and cumulative drifts in generational Markov chains on MNIST. Each plot shows the local drift ( FIDn,n−1 , top) and cumulative drift ( FIDn,0 , bottom) across generations. Results are shown for the label-guided retrained diffusion model (top left), the unconditional retrained diffusion model (top right), and the latent-feedback diffusion model (bottom). Together they illustrate distinct convergence behaviors—rapid stabilization in the label-guided case, continued evolution in the unconditional model, and gradual stationarity in the latent-feedback chain.
Figure 6: Local and cumulative drifts in generational Markov chains on ImageNet-5. Each plot displays the local drift ( FIDn,n−1 , top sub-panel) and the cumulative drift ( FIDn,0 , bottom sub-panel) across generations. Results are shown for the latent-feedback diffusion model (left) and the label-guided retrained diffusion model (right). Both chains stabilize quickly, highlighting how the complexity of the dataset can affect the behavior of the chain.
Manifold Behavior
Local Metrics
Global Metric
Dimensional Pattern
Local
Global
σintra
mLB
PRG
Semantic Expansion Regime
Expansion
Expansion
↑
↑
↑
Coherent Expansion (CE)
Expansion
Contraction
↑
↑
↓
Wrinkled Expansion (WE)
Expansion
Expansion
↑
↓
↑
Anisotropic Expansion (AE)
Expansion
Contraction
↑
↓
↓
Oblate Expansion (OE)
Appendix
Table 3: Latent - manifold dynamics under neural resonance. Each row lists a distinct combination of directional change in the local spread ( σintra ), the local curvature measure ( mLB ), and the global participation ratio ( PRG ). Patterns are grouped into two regimes—semantic expansion ( σintra increasing) and semantic contraction ( σintra decreasing)—and each is labeled according to its geometric character (e.g., coherent expansion, wrinkled contraction). An animation illustrating these patterns is provided in the Supplementary Video.
Figure 7: t-SNE visualization of generational Markov chains on MNIST. Each plot shows the two-dimensional t-SNE embedding of samples drawn from a generational Markov chain, grouped into ten clusters based on latent-space proximity rather than digit class. For the label-guided and unconditional retrained models, the first generation is trained on the MNIST training set and each subsequent generation uses 50,000 images. The latent-feedback chain starts from the MNIST test set, with 10,000 images per generation.
Figure 8: Dimensional pattern of a functional analogue of Lucier’s feedback GMC. We track the dimensional pattern of the GMC using three metrics— σintra , mLB , and PRG —computed in the Wav2Vec 2.0 latent space for an audiobook of War and Peace convolved with OpenAIR impulse-response signals. In the early phase the latent manifold undergoes a wrinkled expansion, followed by an oblate expansion in the middle phase, and a wrinkled contraction in the final phase, nearly reducing PRG to zero and driving mLB to very large values. The chain does not exhibit neural resonance.
Figure 9: Dimensional pattern of CycleGAN GMC From left to right, the plot tracks intra-class spread, local and global dimensions on Horse-Zebra dataset for 200 iterations.
Figure 10: Dimensional pattern of GMCs on MNIST dataset. From left to right, the plot tracks intra-class spread, local and the global dimensions of latent-feedback (blue, 200 iterations), label-guided retrained (orange, 100 iterations) and unconditional retrained (green, 100 iterations) GMCs.
Figure 11: Dimensional pattern of GMCs on ImageNet-5 dataset. From left to right, the plot tracks intra-class spread, intrinsic dimensionality and global dimensions of the latent-feedback (blue, 50 iterations) and label-guided retrained (orange, 11 iterations) diffusion models.
The proliferation of generative artificial intelligence has given rise to an interactive learning environment, where model parameters are continuously updated using not only data generated by natural processes, but also synthetic outputs produced by other models. This paradigm introduces two major challenges: (1) training data are no longer drawn exclusively from the target population, undermining a core assumption of classical statistical learning, and (2) model training processes become inherently correlated, as models interact with one another through repeated exposure to each other's synthetic outputs in a potentially complex manner. Establishing reliable statistical inference in such structured interactive learning environments therefore remains an important open problem. In particular, there is growing concern about model collapse, a phenomenon in which the performance of generative models progressively degrades as they are trained on synthetic data produced by earlier model generations. Prior work on model collapse primarily focuses on a single model trained on its own output, failing to capture model performance in multi-model interactive settings. In this work, we fill this gap by investigating the performance of generative models in an interactive learning environment with general interaction patterns. In particular, we formalize model interactions using directed graphs and show that the occurrence of model collapse depends critically on the topology of the interaction graph. We further derive an explicit necessary and sufficient condition characterizing when model collapse occurs, and establish finite-sample results for linear regression and asymptotic guarantees for general M-estimators. We support our theoretical findings through extensive numerical experiments.
Yuchen Wu, Kangjie Zhou, Weijie Su
School of Operations Research and Information Engineering, Cornell University · Department of Statistics, Columbia University · Department of Statistics and Data Science, University of Pennsylvania
Since 2023, computer scientists have warned against model collapse -- the contamination of training sets with AI-generated outputs that progressively degrade model performance. Exemplifying a positive-feedback-driven failure, it produces effects such as word repetition or pixel noise, ultimately leading to a loss of meaning and coherence -- at least from an engineering standpoint. From a creative one, however, collapse is not merely a breakdown: it also functions as a recursive mirror that recalls early analog video feedback experiments, raising once again the question of what happens when a system turns inward and sees itself. In such cases, so-called machine vision no longer transmits the world (as in tele-vision) but increasingly generates worlds from within. Drawing on media archaeology through case studies of both historical video synthesis techniques and contemporary artistic uses of machine learning, this paper examines what recursive training reveals about the dependent nature of AI-generated data. It argues that the potential effects of collapse challenge transhumanist ideals while inviting an aesthetic perspective, positioning noise and recursion as key concepts for understanding both artmaking and the AI ecosystem. Distributing agency across scales and networks, the latter currently remains reliant on new human-produced content, particularly within foundation models trained on massive datasets.
Violaine Boutet de Monvel
LIRA, IRCAV · Bibliotheca Hertziana – Max Planck Institute for Art History · MPRG Impett – Machine Visual Culture: Artificial Intelligence and the History of Seeing
Conditional image-to-image generators are single-shot: they map input features to an output in one forward pass and treat it as final, with no opportunity to improve on it. Although trained to produce the best possible result in one step, such a model leaves room for improvement if it can adaptively revise its own output over iterations. We propose Recursive Refinement via Feedback Conditioning (RRFC), a novel feedback-conditioning framework for iterative output refinement that teaches a model to adaptively revise its output by conditioning on a new signal, namely its most recent previous prediction, which is fed back as an auxiliary set of channels alongside the original input. This preserves the generator's core architecture while modifying its conditioning interface and, depending on the model family, its training or inference procedure, so RRFC can be attached to existing generators without redesign. We evaluate RRFC across six baselines spanning adversarial, equilibrium, and diffusion-based models and three paired image-to-image translation tasks. Across 18 architecture-task settings, RRFC yields seven Holm-corrected improvements, seven degradations, and four non-significant changes. The gains concentrate on reconstruction-fidelity and identity settings, while five of the seven degradations fall on the single semantic-layout task, where every model declines. These results indicate that feedback-based refinement helps when its objective overlaps with the evaluated property, and that its gains concentrate on the tasks where that overlap holds.
Kareem Hassani, Chaymaa Abbas, Hadi Al Mubasher +1
Department of Electrical and Computer Engineering, American University of Beirut, Riad El-Solh, Beirut 1107 2020, Lebanon