Understanding Diffusion models: Optimization Objective

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Diffusion models are recent state-of-art models (SOTA) employed for generating images via text prompts. The loss function of diffusion models is particularly challenging to understand and is obscured by a lot of mathematical details in original research articles and blogs. The aim of this report is to simplify this step to better understand the objective functions or diffusion models which can employed in a wide variety of scenarios and to understand the new literature which is emerging in this field of generated modelling.

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Prior to the beginning of a discussion about diffusion models, we need to highlight the current frameworks which are being investigated for generative modelling and image synthesis

1. Generative adversarial networks (GAN): Use adverse training using two networks generator and discriminator to train on adversarial loss. There main advantage is the they allow fast sample generation but are hard to train, there concerns related to sample diversity.
2. Variational autoencoders (VAE: Employ two bottleneck approach where the original data x is represented by a latent z variable via the use of a neural network with parameter Φ…