Energy‑based models (EBMs) define a distribution via a scalar energy $E_\theta(x)$ as $p_\theta(x)\propto\exp(-E_\theta(x))$, and this tutorial uses them as a single lens to link the diverse branches of machine learning. An EBM is determined by three choices: the energy function itself, the inference procedure that samples from or optimizes the energy, and the learning method that fits the energy to data. We first develop these components, covering sampling, variational inference, and learning via maximum likelihood, noise‑contrastive estimation, pseudolikelihood, score matching, and adversarial training, and show that all these learning strategies share a contrastive structure. We then demonstrate that discriminative models, GANs, normalizing flows, diffusion and autoregressive models, representation learning approaches such as contrastive learning, word2vec, BERT, denoising auto‑encoders, diffusion representations, reinforcement learning with EBM policies and world models, inverse reinforcement learning, planning, and inference‑time verifiers are all instances of EBMs that differ mainly in how they handle the partition function and sampling. This perspective not only unifies existing methods but also suggests new algorithms by swapping a single component while keeping the others fixed, and composing energies offers a principled way to combine learned models at inference time.
Review: By casting a wide range of models into a common energy‑based framework, the article clarifies their underlying connections and opens avenues for modular algorithm design and model composition.