Generative Modeling: From Data Distributions to Deep Generative Models
If you approach generative models as ""networks that create images,"" the field quickly turns into a collection of disconnected architectures. A more useful developer mental model starts one level lower: What probability structure could have produced the data, and how can we represent, learn, and infer that structure without making the computation impossible? That question connects autoregressive models, VAEs, flow-based models, GANs, and diffusion models. Their architectures look very different, but they all respond to the same underlying tension: high-dimensional data distributions are difficult to represent, learn, normalize, sample from, and reason about. Generative modeling can therefore be organized around three interacting problems: Representation: How do we represent a complex high-dimensional joint distribution? Learning: How do we make the model distribution approach the data distribution? Inference: Given an observation, how do we reason backward about hidden variables or the process that generated it? Once these three pieces are connected, the major families of deep generative models become much easier to understand. From prediction to distribution learning A discriminative model usually begins with a prediction problem. Given an input x , predict the most likely output y : f ( x ) = y ar g max p ( y ∣ x ) The model focuses directly on the conditional relationship required for prediction. A generative model asks a broader question. Instead of learning only the path from x to y , it models the probability structure from which the data arises. For class-conditional modeling, for example, we can model p ( x ∣ y ) together with the prior p ( y ) and recover the posterior using Bayes' rule: p ( y ∣ x ) = p ( x ) p ( x ∣ y ) p ( y ) In unsupervised generative modeling, the target becomes the data distribution itself. We assume the training samples come from some unknown distribution: x 1 , x 2 , … , x N ∼ i.i.d. p data ( x ) The model then construc