Google Research explains why diffusion models don't just memorize
A paper presented at ICLR 2026 traces the mathematical roots of generative creativity in diffusion models to a smoothing effect inherent in neural network training.
Why do diffusion models generate new images instead of copying their training data?
Diffusion models create genuinely novel outputs because neural network training naturally produces a "smoothed" version of the function that guides the denoising process. That smoothing pushes generated samples to fall between training examples along the underlying data manifold, rather than landing on any single memorized example.
The core mechanics
Training a diffusion model starts by corrupting real data, say photos, with increasing amounts of noise until nothing recognizable remains. The model is then trained to reverse that process step by step, reconstructing a plausible image from pure noise.
The key mathematical object here is the score function, which acts as a force field that pulls noisy data points toward realistic outputs during generation. A perfectly learned score function, derived exactly from training samples, would steer every generated sample back to a training example, producing copies rather than novel images.
Where smoothing enters
In practice, neural networks do not learn an exact score function. According to the paper "On the Interpolation Effect of Score Smoothing in Diffusion Models," presented at ICLR 2026, they learn a smoothed approximation of it. That smoothing is not a bug or an accident; it is a direct consequence of how neural network optimization works.
The smoothed score function redirects generated samples away from memorized training points and toward positions that interpolate between them along the hidden structure of the data. Google Research scientist Zhengdao Chen describes this as the mathematical source of the model's creative behavior.
The researchers use a gas-particle analogy to make the idea concrete: think of noisy data as gas particles scattered in a room, with the score function acting as a force field that directs each particle. A perfectly sharp force field funnels particles to exact training-data locations. A smoothed one guides them to intermediate positions, producing outputs that are consistent with the data distribution without duplicating any specific example.
Why this matters for understanding generative AI
Most discussion of diffusion model behavior treats creativity as an emergent mystery. This work argues it is instead a predictable mathematical consequence of standard training, which has practical implications for both capability and safety research.
If memorization versus generalization is governed by how much smoothing occurs in the learned score function, then researchers have a concrete handle for studying when a model will copy training data (a privacy and copyright concern) versus when it will interpolate to something new. Understanding the mechanism also opens a path toward controlling that trade-off deliberately.
The paper connects to a broader effort to reduce the "black-box" character of diffusion-based generative AI by grounding observed behaviors in mathematics rather than intuition. The team has released both the paper and accompanying code, links to which appear on the Google Research blog post.
What the research does not claim
The source documents do not specify quantitative benchmarks comparing memorization rates under different smoothing conditions, nor do they describe experiments on particular image datasets beyond using cat photos as an illustrative example. The work is framed as a theoretical explanation built on prior research literature, not an empirical study reporting new performance figures.
The finding applies to diffusion models broadly, covering applications from image generation to molecular discovery, both of which the researchers cite as domains where these models have demonstrated the ability to generalize beyond training data.