Explore the intricacies of Latent Variable Energy Based Models (LV-EBMs) with a focus on inference in this comprehensive lecture. Delve into topics such as affine transformations, training sample mappings, and the unconditional case. Discover the energy function and its applications, including indexing by individual training samples and analyzing specific energy shapes. Examine the concept of free energy, its definition, and practical examples. Learn how to compute free energy across the entire space. Gain valuable insights into LV-EBMs through clear explanations and visual demonstrations using a graphic tablet.