A Markovian View of Iterative-Feedback Loops in Image Generative Models: Neural Resonance and Model Collapse

Vibhas Kumar Vats; David J. Crandall; Samuel Goree

cs.LGFeb 22, 2026

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

Abstract

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. $X_{n}$ 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	$\sigma_{intra}$	$m_{LB}$	$PR_{G}$
Semantic Expansion Regime
Expansion	Expansion	$\uparrow$	$\uparrow$	$\uparrow$	Coherent Expansion (CE)
Expansion	Contraction	$\uparrow$	$\uparrow$	$\downarrow$	Wrinkled Expansion (WE)
Expansion	Expansion	$\uparrow$	$\downarrow$	$\uparrow$	Anisotropic Expansion (AE)
Expansion	Contraction	$\uparrow$	$\downarrow$	$\downarrow$	Oblate Expansion (OE)

Table 1: Latent - manifold dynamics under neural resonance. Each row lists a distinct combination of directional change in the local spread (

\sigma_{intra}

), the local curvature measure (

m_{LB}

), and the global participation ratio (

PR_{G}

). Patterns are grouped into two regimes, semantic expansion (

\sigma_{intra}\uparrow

) and semantic contraction (

\sigma_{intra}\downarrow

), 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 ( $FID_{n,n-1}$ ) shows local drift between successive generations, and the orange curve ( $FID_{n,0}$ ) 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. $X_{n}$ represents the current distribution of images at generation $n$ and $T(\cdot)$ 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 ( $FID_{n,n-1}$ , top) and cumulative drift ( $FID_{n,0}$ , 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 ( $FID_{n,n-1}$ , top sub-panel) and the cumulative drift ( $FID_{n,0}$ , 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	$\sigma_{intra}$	$m_{LB}$	$PR_{G}$
Semantic Expansion Regime
Expansion	Expansion	$\uparrow$	$\uparrow$	$\uparrow$	Coherent Expansion (CE)
Expansion	Contraction	$\uparrow$	$\uparrow$	$\downarrow$	Wrinkled Expansion (WE)
Expansion	Expansion	$\uparrow$	$\downarrow$	$\uparrow$	Anisotropic Expansion (AE)
Expansion	Contraction	$\uparrow$	$\downarrow$	$\downarrow$	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 (

\sigma_{intra}

), the local curvature measure (

m_{LB}

), and the global participation ratio (

PR_{G}

). Patterns are grouped into two regimes—semantic expansion (

\sigma_{intra}

increasing) and semantic contraction (

\sigma_{intra}

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—

\sigma_{intra}

m_{LB}

, and

PR_{G}

—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

PR_{G}

to zero and driving

m_{LB}

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.

Markov Chains

See all 29 papers

When Does Model Collapse Occur in Structured Interactive Learning?
May 19, 2026Yuchen Wu, Kangjie Zhou, Weijie SuModel Collapse Generative Modeling
School of Operations Research and Information Engineering, Cornell University · Department of Statistics, Columbia University · Department of Statistics and Data Science, University of Pennsylvania
Model Collapse: On Recursion, Noise, and Uncharted Machine Visions
Jun 22, 2026Violaine Boutet de MonvelModel Collapse Generative Modeling
LIRA, IRCAV · Bibliotheca Hertziana – Max Planck Institute for Art History · MPRG Impett – Machine Visual Culture: Artificial Intelligence and the History of Seeing
RRFC: Recursive Refinement via Feedback Conditioning for Iterative Image-to-Image Generation
Aug 16, 2026Kareem Hassani, Chaymaa Abbas, Hadi Al Mubasher +1Conditional Image Generation Image-to-Image Translation
Department of Electrical and Computer Engineering, American University of Beirut, Riad El-Solh, Beirut 1107 2020, Lebanon

May 19, 2026J/K move · Enter open · S save

When Does Model Collapse Occur in Structured Interactive Learning?

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

Model Collapse Generative Modeling Statistical Learning Theory

Open paper AskPDF arXiv

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.

Abstract

Markov Chains

Explore similar work

When Does Model Collapse Occur in Structured Interactive Learning?

Model Collapse: On Recursion, Noise, and Uncharted Machine Visions

RRFC: Recursive Refinement via Feedback Conditioning for Iterative Image-to-Image Generation