How Diffusion Models Transform Noise into Stunning AI Images

How the AI photo generation process works step-by-step

From random noise to a structured image

The basic principle of diffusion models is a process that can be described as 'reverse time'. While in the real world, structure gradually decays into chaos (entropy increases), diffusion models work in reverse:

1. Initialization with random noise: The process begins with pure noise - random pixels without any structure or meaning.
2. Gradual denoising: The model systematically transforms this noise into an increasingly structured image over a series of steps.
3. Guided process: During each iteration, the model estimates what a 'less noisy' image should look like, relying on knowledge gained during training.
4. Conditional generation: The entire process can be guided by a text input (prompt) that specifies what the resulting image should contain.

The 'forward diffusion' vs. 'reverse diffusion' process

When training diffusion models, two interconnected processes occur:

1. Forward diffusion: Training images are gradually noised until they become pure noise. The model learns how this process works.
2. Reverse diffusion: The real magic happens during generation, where the model applies the learned knowledge in the opposite direction - gradually removing noise until a clean image emerges.

                    Original Image → Add Noise → More Noise → ... → Pure Noise
                    ↓                                                     ↑
                    Model Training                                        ↑
                    ↓                                                     ↑
                    Generated Image ← Less Noise ← Less Noise ← ... ← Pure Noise
                

Sampling and the number of generation steps

The quality of the resulting image often depends on the number of generation steps (so-called sampling steps):

• Low number of steps (e.g., 20-30): Faster generation, but possible artifacts and lower detail quality.
• High number of steps (e.g., 50-100): Higher quality and detail consistency, but longer generation time.

In practice, advanced sampling methods like DDIM, PLMS, or DPM-Solver are often used, which can achieve high-quality results even with a lower number of steps.

What are latent diffusion models and why they revolutionized AI image creation

From pixel space to latent space

A breakthrough moment in the development of diffusion models was the transition from working in pixel space to the so-called latent space:

• Pixel space: Direct work with the RGB values of individual pixels - computationally expensive, requires an enormous amount of memory.
• Latent space: A compressed representation of the image where only the most important features are preserved - significantly more efficient.

Latent Diffusion Models (LDM)

Latent Diffusion Models, introduced in 2022, brought a fundamental breakthrough:

1. Dimensionality compression: The input image is first converted by an encoder into a latent space with much lower dimensionality.
2. Diffusion in latent space: The diffusion process takes place in this compressed representation, dramatically reducing computational requirements.
3. Decoding the result: The final latent representation is converted back into pixel space by a decoder as the resulting image.

Why LDMs meant a revolution

• Computational efficiency: Memory requirements reduced by up to 95% compared to pixel-space diffusion models.
• Faster training: Ability to train on much larger datasets with available resources.
• Modularity: Separating the compression process from the diffusion itself allowed for a more flexible architecture.
• Democratization of technology: Thanks to lower requirements, tools accessible to the general public could emerge (Stable Diffusion).

It was Stable Diffusion, based on the LDM architecture, that kicked off the massive expansion of generative AI tools in 2022 due to its openness and relatively low hardware requirements.

What mathematical principles underlie the ability of AI generators to create photorealistic content

Stochastic Differential Equations

At the core of diffusion models lies a sophisticated mathematical apparatus:

• SDEs (Stochastic Differential Equations): Describe the process of gradually adding noise to an image as a continuous process.
• Fokker-Planck equation: A mathematical tool that describes the evolution of probability distributions over time.

U-Net architecture

A key element of most diffusion models is a U-Net type neural network:

• Encoder-decoder with skip connections: Allows preserving structural information during compression and subsequent reconstruction.
• Attention mechanisms: Enable the model to focus on relevant parts of the image and capture long-range dependencies.

Control mechanisms and conditional generation

The ability to generate images according to text prompts requires additional components:

• Cross-attention: A mechanism that links text embeddings with visual features in the latent space.
• CLIP embeddings: Utilization of pre-trained models (like CLIP from OpenAI) that can bridge the text and visual domains.

Variational inference

Diffusion models can be understood as a form of variational inference:

• Maximization of posterior probability: The model attempts to maximize the probability that the generated image comes from the same distribution as the training data.
• Score-based generative modeling: A modern approach that models the gradient of the log-probability of the data distribution.

Mathematically, the reverse diffusion process can be expressed as solving the equation:

                    dx = [f(x,t) - g(t)²∇ₓlog p(x,t)] dt + g(t) dw
                

where f and g are functions of time, ∇ₓlog p(x,t) is the so-called score function, and dw represents the Wiener process.

How different types of diffusion models used in popular AI graphics tools differ

Pixel-space vs. Latent Diffusion Models

• DALL-E (first version): Utilized diffusion in pixel space, which required huge computational resources and limited resolution.
• Stable Diffusion: Pioneer of latent diffusion, dramatically reduced requirements and enabled public use.
• DALL-E 2 and 3: Hybrid approaches combining principles of latent diffusion with other techniques.

Differences in architecture and optimization

• Midjourney: Proprietary architecture with an emphasis on aesthetic quality, likely uses a highly optimized version of diffusion models.
• Imagen (Google): Uses cascaded diffusion models with progressive resolution enhancement.
• Stable Diffusion XL: An enhanced version of the classic SD with larger models and a multi-stage process.

Specialized diffusion models

In the ecosystem of diffusion models, we also find specialized variants:

• ControlNet: An extension allowing more precise control over the generated content using input conditions like sketches, depth maps, or poses.
• InstructPix2Pix: Specialization in editing existing images according to text instructions.
• DreamBooth: Personalization of diffusion models for a specific identity or object with minimal training data.

Training approaches

• Text-to-Image: Classic models trained on paired datasets of images and their descriptions.
• Image-to-Image: Models specialized in transforming an input image according to instructions.
• Self-supervised: Newer approaches utilizing learning without explicit labels.

The future of diffusion models in image generation

Diffusion models are undergoing rapid development, and we can expect further progress in several directions:

• Higher efficiency: Further optimizations will enable generation at higher resolutions and with fewer steps.
• More precise control: Development is moving towards finer control over every aspect of the generated image.
• Multimodal models: Integration with other modalities such as video, 3D, or audio.
• On-device inference: Optimization for running on mobile devices and standard computers.

Conclusion

Diffusion models represent a fascinating area of artificial intelligence that has surpassed many expectations regarding the capabilities of machine learning. Their ability to transform noise into structured, photorealistic images has opened up new possibilities for creative work and visual communication. With ongoing research and development, we can expect these technologies to play an increasingly significant role in the digital world. Explore further technological aspects of AI image generators in our comprehensive overview.

Latent diffusion models then marked a key turning point, democratizing access to this technology and enabling its mass adoption. The mathematical principles they are based on represent an elegant application of advanced concepts of probability and statistics in a practical tool available to the general public.

Whether you are an artist, designer, marketer, or just an enthusiast of new technologies, understanding how diffusion models work will allow you to better leverage their potential and perhaps even contribute to their further development.