Probabilistic modeling of data is the core in machine learning and modern generative AI. This survey reviews the methodological evolution from traditional statistical formulations to recent deep generative frameworks under a unified view of probability distribution learning. Representative methods are organized into three connected routes： Maximum-likelihood-based modeling， score-matching-based modeling， and flow-based modeling. On the traditional side， the survey revisits Gaussian assumptions， Gaussian mixture models， expectation-maximization （EM） algorithms， and variational inference， emphasizing how tractability-flexibility trade-offs shape model design. On the modern side， it discusses variational autoencoders （VAEs）， generative adversarial net （GAN）-related generative mechanisms， diffusion probabilistic models， score-based stochastic differential equation （SDE） formulations， normalizing flows， and flow matching， with focus on objective functions， parameterization choices， and sampling dynamics. A structured comparison is provided from the perspectives of explicit likelihood， trajectory modeling， computational efficiency， controllability， and deployment stability. To bridge methodology and practice， the paper summarizes benchmark-oriented observations and application trends in image generation， video and audio synthesis， inverse problems， and science-and-control scenarios. It also identifies practical bottlenecks， including dependence on high-quality large-scale data， limited semantic operability of latent representations， and inference latency caused by multi-step sampling. Finally， future directions are discussed around coordinated advances in path design， training objectives， numerical solvers， and guidance strategies， together with unified evaluation over quality， efficiency， safety， and compliance for trustworthy large-scale deployment.