The uniformity of the result facilitates a versatile recovery
In the real world, complex data such as high-resolution images live in high-dimensional pixel spaces rather than a simple one-dimensional world. However, the vast majority of this space is just random noise that is meaningless to the human eye. Only a small fraction of the data points in this space correspond to recognizable images, and they live in the so-called Data manifold (Like a sheet of paper tucked inside a larger space). The model does not know the shape and location of the data collector in advance. Thus, image generation can be viewed as a task Diversified recoveryThe model needs to infer the shape of the hidden data manifold based on the limited number of training data taken from it, and then come up with new points on the manifold that will correspond to new, meaningful images. It turns out that outcome homogeneity is crucial for diffusion models to achieve this.
Strikingly, in multidimensional settings, the effect of outcome smoothing emerges in a direction-dependent manner. along parallel directions (or “tangential“) for the hidden data manifold, it produces a similar hysteresis effect as in the 1D scenario. However, along directions pointing toward the manifold, the “ideal” score function is already relatively smooth (in fact, just a straight line if the manifold is flat), and further smoothing does not make much difference.
So, instead of suppressing the flow of particles in every direction (which would stop them in noisy empty space and blur the final images), smoothing the dots does not slow them down. Convergence towards the manifold, but only reduces their tendency to collapse towards the training data along tangential directions. In this way, the model strikes a balance between quality and freshness: images look realistic (because they have successfully arrived at the meaningful data set) and fresh (because they have settled into the empty spaces between the original training data points).
