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Understanding Diffusion Models: Explaining the Mathematics behind Them from Basics

The Fascinating World of Diffusion Models: A Comprehensive Overview of State-of-the-Art Image Generation

Diffusion models are a new class of state-of-the-art generative models that have shown remarkable success in generating high-resolution images. They have gained popularity after being implemented by big organizations such as OpenAI, Nvidia, and Google. Some example architectures that have been built based on diffusion models include GLIDE, DALLE-2, Imagen, and the open-source stable diffusion.

The main principle behind diffusion models lies in decomposing the image generation process into many small “denoising” steps. The model gradually corrects itself over these steps to produce high-quality samples. While this idea of refining the representation has been utilized in models like AlphaFold, diffusion models offer a unique approach that sets them apart.

The diffusion process involves gradually adding Gaussian noise to the input image through a series of steps. A neural network is then trained to reverse this process, allowing the generation of new data. This reverse diffusion process is the core of the model’s sampling mechanism.

Different approaches, such as Denoising Diffusion Probabilistic Models (DDPM) and stable diffusion models, have been proposed to tackle the challenges in training diffusion models. Cascade diffusion models and latent diffusion models are also employed to scale up diffusion models to high resolutions.

Moreover, guided diffusion models leverage the conditioning of the sampling process on image labels or text embeddings to guide the generation of samples. This conditioning helps steer the model towards specific characteristics desired in the generated samples.

Lastly, score-based generative models, which operate through score matching and Langevin dynamics, offer an alternative approach to generative learning. The use of Noise Conditional Score Networks (NCSN) and stochastic differential equations (SDE) expands the capabilities of score-based generative models for high-fidelity image generation.

Overall, diffusion models represent a promising direction in the field of generative modeling, offering a unique and effective approach to generating diverse and high-quality images. By understanding the principles and techniques behind diffusion models, researchers and developers can leverage these advancements to create innovative and realistic visual content.

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