LatentLatentlatent variable variables—unobservedVariablelatent variable factors that influence observable data—play a critical role in understanding complex phenomena across various fields, including causal inferenceInference and machine learningLearningmachine learning. This chapter explores the concept ofVariablelatent variable latent variablesLatentlatent variable and their significance in modeling hiddenHidden structures that affect observed variables. Through illustrative examples, it highlights how Variablelatent variable latent variablesLatentlatent variable can explain apparent correlations that are not causative, emphasizing their importance in domains such as drug discovery and causal analysis. Focusing on machine learningLearningmachine learning, this chapter introduces variational inferenceVariationalvariational inference as a principled framework for estimating distributionsDistribution overVariablelatent variable latent variablesLatentlatent variable conditioned on observed data. It covers the theoretical foundations of variational Inferenceinference, including theEvidence lower bound (ELBO) Evidence Lower BoundBoundevidence lower bound (ELBO) (ELBO) and expectation maximizationExpectationexpectation maximization (EM). This chapter further delves into variational modelsVariationalvariational model, with particular emphasis onVariationalvariational autoencoder Variational AutoencodersAutoencodervariational autoencoder (VAEs). VAEs combine neural networksNeural network with probabilistic inferenceInference to learn latent spacesLatentlatent space, enabling both data generation and representationRepresentation learning. They are foundational in modern generative modeling, though newer extensionsExtension (such as hierarchical VAEs, adversarial VAEs, and diffusion modelsDiffusiondiffusion model) continue to expand the field.