How Diffusion Models Memorize

Abstract: Despite their success in image generation, diffusion models can memorize training data, raising serious privacy and copyright concerns. Although prior work has sought to characterize, detect, and mitigate memorization, the fundamental question of why and how it occurs remains unresolved. In this paper, we revisit the diffusion and denoising process and analyze latent space dynamics to address the question: "How do diffusion models memorize?" We show that memorization is driven by the overestimation of training samples during early denoising, which reduces diversity, collapses denoising trajectories, and accelerates convergence toward the memorized image. Specifically: (i) memorization cannot be explained by overfitting alone, as training loss is larger under memorization due to classifier-free guidance amplifying predictions and inducing overestimation; (ii) memorized prompts inject training images into noise predictions, forcing latent trajectories to converge and steering denoising toward their paired samples; and (iii) a decomposition of intermediate latents reveals how initial randomness is quickly suppressed and replaced by memorized content, with deviations from the theoretical denoising schedule correlating almost perfectly with memorization severity. Together, these results identify early overestimation as the central underlying mechanism of memorization in diffusion models.

• The paper reveals that classifier-free guidance induces early overestimation, which drives memorization beyond traditional overfitting.
• It introduces a latent decomposition framework that quantifies memorization using SSCD scores and covariance analysis of denoised latents.
• The study suggests that adaptive guidance schedules can mitigate memorization by preserving latent diversity during the denoising process.

Mechanisms of Memorization in Diffusion Models

Introduction

The paper "How Diffusion Models Memorize" (2509.25705) provides a rigorous analysis of memorization phenomena in text-to-image diffusion models, with a particular focus on the denoising dynamics and latent space trajectories. The authors challenge the prevailing notion that memorization is solely a consequence of overfitting, and instead identify early overestimation—amplified by classifier-free guidance—as the central mechanism driving memorization. The study leverages Stable Diffusion v1.4, v2.1, and RealisticVision, employing SSCD metrics to quantify memorization severity and introduces a decomposition framework for latent analysis.

Memorization Beyond Overfitting

The conventional view attributes memorization in generative models to overfitting, where the model's outputs closely match training samples due to excessive capacity or insufficient regularization. The authors demonstrate that, in diffusion models, memorization cannot be explained by overfitting alone. Specifically, when classifier-free guidance is applied (guidance scale $g > 1$), the training loss is paradoxically larger for memorized samples during early denoising steps, despite stronger memorization.

Figure 1: Guidance amplifies the presence of $\mathbf{x}$; classifier-free guidance ($g=7.5$) increases both cosine similarity and $\ell_2$ proximity between denoised latents and the memorized image.

Empirical results show that, without guidance ($g=1.0$), memorized samples exhibit lower $\ell_2$ error, consistent with overfitting. However, with guidance, the error increases in early steps, yet SSCD scores—indicating memorization—are higher. This contradiction highlights that memorization is not a simple function of training loss minimization.

Role of Classifier-Free Guidance and Overestimation

Classifier-free guidance, a standard technique for improving sample fidelity, linearly amplifies the conditional noise prediction. The authors show that, under memorized prompts, the conditional noise predictor injects a scaled version of the training image into the denoising process, resulting in overestimation. This effect is formalized as:

$\hat{\mathbf{x}}_0^{(T)} \approx g \mathbf{x}$

where $g$ is the guidance scale. The magnitude of overestimation grows linearly with $g$, directly elevating the training loss and accelerating convergence toward the memorized image.

Figure 2: Lack of guidance degrades quality; images generated without guidance ($g=1.0$) are less realistic and less memorized compared to those with guidance ($g=7.5$).

Figure 3: Guidance drives memorization; SSCD scores are consistently higher with classifier-free guidance.

Latent Space Dynamics and Diversity Collapse

The paper introduces a decomposition of intermediate latents:

$$\mathbf{x}_t = \sqrt{\bar{\alpha}_t} \mathbf{x} + \sqrt{1 - \bar{\alpha}_t} \mathbf{x}_T$$

where $\mathbf{x}_T$ is the initial noise and $\mathbf{x}$ is the training image. Under memorization, classifier-free guidance causes $w_0^{(t)}$ (the weight of $\mathbf{x}$) to grow faster than the theoretical schedule, while $w_T^{(t)}$ (the weight of $\mathbf{x}_T$) decays prematurely. This results in rapid suppression of randomness and dominance of memorized content.

Figure 4: Faster dominance of $\mathbf{x}$ under memorization; decomposition shows accelerated amplification of the memorized image in the latent trajectory.

The collapse of latent diversity is quantified by the trace of the covariance matrix of denoised latents, which is significantly reduced for memorized prompts. Principal component analysis of latent updates reveals strong alignment with the memorized image direction, indicating deterministic convergence of trajectories.

Quantitative Correlation with Memorization Severity

The authors aggregate decomposition deviations across timesteps and demonstrate near-perfect correlation with SSCD memorization scores (Pearson coefficients $>0.9$). The metrics include excess contribution of $\mathbf{x}$, premature suppression of $\mathbf{x}_T$, and overall deviation from the theoretical denoising schedule.

Figure 5: Decomposition deviations predict memorization severity; strong correlation between SSCD scores and decomposition-based metrics.

Theoretical and Practical Implications

The findings have direct implications for both detection and mitigation of memorization. The magnitude of text-conditional noise predictions is shown to be a principled metric for memorization detection, providing theoretical justification for prior heuristic approaches. Mitigation strategies, such as disabling guidance during early denoising, are explained as mechanisms for preserving latent diversity and preventing premature convergence to memorized samples.

The analysis is robust across different samplers (DDIM, DDPM) and model architectures (SD v1.4, v2.1, RealisticVision), indicating generality of the identified mechanism.

Future Directions

The study suggests that controlling the regime of early denoising—specifically, the timing and magnitude of guidance—can be an effective lever for reducing memorization in diffusion models. Future research may focus on adaptive guidance schedules, regularization of conditional noise predictors, and architectural modifications to preserve diversity. The decomposition framework provides a foundation for further theoretical analysis of generative model dynamics.

Conclusion

This paper establishes that memorization in diffusion models is fundamentally driven by early overestimation of training samples, amplified by classifier-free guidance. The resulting collapse of latent diversity and deterministic convergence to memorized images is quantitatively and theoretically characterized. These insights inform both detection and mitigation strategies, and point toward principled approaches for safer, less replicative generative modeling.