It's funny because while it may be hard for us humans to visualize extra spatial dimensions, many can easily reckon with the concept of a spreadsheet. If you th

It's funny because while it may be hard for us humans to visualize extra spatial dimensions, many can easily reckon with the concept of a spreadsheet. If you think deeply about diffusion art models, you can start to grok extra dimensions in a different sense – things like, composition, tonality, subject matter. My brain can't really comprehend the tesseract-like nature of higher-dimensionality in a spatial sense – but I can get a glimmer of what it means to explore that space along different vectors. How over in this corner of the 'cube' is an image of a dog rendered in the style of Rembrandt. And how if I travel along a particular axis, it's still a dog in the style of Rembrandt, but now it's a funny dog in the style of Rembrandt. And if I turn and travel down a different axis still, it's a funny dog in the style of Rembrandt, at night. In this way, I find diffusion models a really interesting way to think about spaces of hyper dimensionality. It's a bit 'Flat World' – but, it's really helped me visualize how something can be transformed or explored in these 'extra' dimensions.