Google Research: creativity of diffusion models explained as 'score smoothing'

What is a diffusion model and why does it create new images?

A diffusion model is a generative model that creates data by progressively removing noise — starting from random noise and iteratively refining it guided by the score function, a gradient that directs the denoising process toward probable data. Researcher Zhengdao Chen from Google Research has published a mathematical explanation of why these models generate images that are not in the training set.

Regularization leads to “smoothing”

The key mechanism lies in the fact that neural networks do not learn the exact, but an approximate and blurred version of the score function — due to regularization (weight decay) that prevents overfitting. Chen calls this effect “score smoothing.” Instead of denoising particles gravitating exactly toward memorized training examples, they settle in interpolation zones between training points along the data manifold. The result is novel, non-memorized generations — combinations of features the model never saw together.

High dimensions: the balance between realism and novelty

In high dimensions, typical of images, smoothing acts selectively: it slows motion tangentially along the manifold while accelerating motion toward it (perpendicularly). This means the model stays “realistic” by adhering to the data manifold, while retaining novelty by not converging to known points. This geometric balance between realism and originality is not explicitly programmed — it emerges as a direct consequence of regularization during training.

Creativity as a predictable mathematical result

Chen’s conclusion directly challenges the mystification of generative models: the creativity of diffusion models is a predictable mathematical result, not a random emergent phenomenon. Compare with classic interpolation in the latent space of GAN models — there interpolation is explicit, while diffusion models achieve the same effect implicitly through score smoothing. This insight opens a path toward more precise control of creativity: by varying the strength of regularization, one could modulate how “far” from training data a model generates.