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Introduction Generative models can be classified into 2 categories: Implicit models Probability distribution is implicit represented by a network and new samples are generated by passing a Gaussian noise as the input. One example is generative adversarial networks (GANs). Likelihood-based models Directly learn probability distribution density by maximizing likelihood. Examples include variational auto-encoders (VAEs) and diffusion model. We have derive the diffusion model from another page Here. We have introduced score function which is a objective of ELBO optimization....

Likelihood Maximization and ELBO Assume data is generated from some latent variable $z$. It might include higher-level representations such as color and shape. The goal is to use this latent variable to get new samples. We can introduce a joint probability $p(x,z)$ and try to maximize likelihood of p(x) $$p(x)=\int p(x,z)dz$$ Since integration is intractable, we apply Bayes theorem instead. $$p(x)=\frac{p(x,z)}{p(z|x)}$$ True posterior is unavailable to us so we use above equation to derive log likelihood....

Introduction Automated Driving Systems (ADSs) aims to prevent traffic accidents and mitigate congestion 1. ADS is empowered by recent development of Deep Learning and sensor modalities (such as lidar).DARPA Grand Challenge is the first major competition in this field where human interation is prohibited. However the environment is relatively simple. Society of Automotive Engineers (SAE) defined five levels of driving automation from L0 to L5. L1 include simple tasks such as adaptive cruise control....