Research text on diffusion models says score smoothing facilitates manifold recovery, describing how image generation works in high-dimensional pixel spaces where most points are random noise and only a small fraction correspond to recognizable images.
The source explains that these meaningful images lie on a data manifold, whose shape and location are not known to the model in advance. Image generation is described as a task of manifold recovery, where a model must infer the hidden data manifold from a finite set of training samples and then generate new points on that manifold.
According to the text, score smoothing is crucial for diffusion models to do this. In multi-dimensional settings, its effect depends on direction. Along directions parallel, or “tangential”, to the hidden data manifold, smoothing slows movement in a similar way to the 1-D case. Along directions pointing toward the manifold, the “perfect” score function is already relatively smooth, so further smoothing has little effect.
The source says this means score smoothing does not slow motion toward the manifold. Instead, it reduces the tendency of particles to collapse toward the training data along tangential directions. The result is described as a balance between quality and novelty: images are realistic because they reach the meaningful data manifold, while also being new because they settle into spaces between the original training data points.
Source: research.google.
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