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The base diffusion model can only generate unconditionally from the whole distribution. For example, a diffusion model learned on ImageNet would generate images that look like a random image from ImageNet. To generate images from just one category, one would need to impose the condition, and then sample from the conditional distribution.
An example of a directed, cyclic graphical model. Each arrow indicates a dependency. In this example: D depends on A, B, and C; and C depends on B and D; whereas A and B are each independent. The next figure depicts a graphical model with a cycle. This may be interpreted in terms of each variable 'depending' on the values of its parents in some ...
Bernoulli (bond) percolation on complete graphs is an example of a random graph. The critical probability is p = 1 / N , where N is the number of vertices (sites) of the graph. Bootstrap percolation removes active cells from clusters when they have too few active neighbors, and looks at the connectivity of the remaining cells. [20]
Diffusion curves are vector graphic primitives for creating smooth-shaded images. Each diffusion curve partitions the 2D graphics space through which it is drawn, defining different colors on either side. When rendered, these colors then spread into the regions on either side of the curve in a way analogous to diffusion. The colors may also be ...
It is used heavily in statistical physics, statistical analysis, information theory, data science, neural networks, finance and marketing. A sample path of a diffusion process models the trajectory of a particle embedded in a flowing fluid and subjected to random displacements due to collisions with other particles, which is called Brownian motion.
There are two special cases of the Bass diffusion model. The first special case occurs when q=0, when the model reduces to the exponential distribution. The second special case reduces to the logistic distribution, when p=0. The Bass model is a special case of the Gamma/shifted Gompertz distribution (G/SG): Bemmaor [9] (1994)
Diagram of the latent diffusion architecture used by Stable Diffusion The denoising process used by Stable Diffusion. The model generates images by iteratively denoising random noise until a configured number of steps have been reached, guided by the CLIP text encoder pretrained on concepts along with the attention mechanism, resulting in the ...
When an orbital diagram is drawn for the logistic map, it is possible to see how the branch representing the stable periodic orbit splits, which represents a cascade of period-doubling bifurcations. Bifurcation diagram of the period-doubling bifurcation cascade occurring between parameters r 1 = 3 {\displaystyle r_{1}=3} and a ∞ = 3.56994 ...