[Phase 3] Implement Self-Supervised Learning Methods

Open ooples opened this issue 2 months ago • 1 comments

Problem

COMPLETELY MISSING: Self-supervised learning is critical for learning from unlabeled data.

Missing Implementations

Contrastive Methods (CRITICAL):

SimCLR (Simple Framework for Contrastive Learning)
MoCo (Momentum Contrast)
MoCo v2, MoCo v3

Non-Contrastive (HIGH):

BYOL (Bootstrap Your Own Latent)
SimSiam
Barlow Twins

Vision SSL (HIGH):

DINO (Self-Distillation with No Labels)
iBOT
MAE (Masked Autoencoder)

Multimodal (HIGH):

CLIP enhancements (issue #272 has CLIP)
ALIGN
Florence

Architecture

src/SelfSupervisedLearning/
Interface: ISSLMethod, IContrastiveLoss
Augmentation integration
Pre-training + fine-tuning pipeline

Success Criteria

ImageNet linear evaluation protocol
Transfer learning benchmarks
Parity with VISSL / Lightly

Nov 07 '25 03:11 ooples

Junior Developer Implementation Guide: Issue #395

Diffusion Models (DDPM, Stable Diffusion)

Overview

This guide will walk you through implementing Diffusion Models for AiDotNet. Diffusion models are state-of-the-art generative models that create high-quality images by learning to reverse a gradual noising process. They power tools like Stable Diffusion, DALL-E 2, and Midjourney.

Understanding Diffusion Models

What Are Diffusion Models?

Diffusion models work like a "reverse movie" of image destruction:

Forward Process (Diffusion): Take a real image and gradually add Gaussian noise over many timesteps until it becomes pure random noise. This is a fixed mathematical process (no learning involved).
Reverse Process (Denoising): Train a neural network to reverse this process - start with random noise and gradually remove it step by step to generate a realistic image.

Real-World Analogy:

Forward: Like a photograph slowly fading and becoming grainy over 1000 days
Reverse: Training an AI to restore the original photograph from the grainy version, one day at a time

Why Diffusion Models Are Powerful

High Quality: Generate photorealistic images with fine details
Stable Training: More stable than GANs (no mode collapse, adversarial issues)
Flexible: Can be conditioned on text, images, or other inputs
Interpretable: The gradual denoising process is easier to understand than GAN's single-step generation

Key Concepts

1. Forward Diffusion Process (Adding Noise)

Given a clean image x₀:
- At timestep t, add Gaussian noise to create x_t
- The amount of noise is controlled by a noise schedule (β₁, β₂, ..., β_T)
- At t=T (final timestep), x_T is pure Gaussian noise

Mathematical formulation:
x_t = √(ᾱ_t) · x₀ + √(1 - ᾱ_t) · ε

Where:
- ε ~ N(0, I) is random Gaussian noise
- ᾱ_t = ∏(1 - β_s) for s=1 to t
- β_t is the noise schedule at timestep t

Key Insight: We can sample x_t directly from x₀ (no need to go through all intermediate steps)!

2. Noise Schedules

Controls how fast noise is added:

Linear Schedule:

β_t increases linearly from β_start to β_end
Example: β_start = 0.0001, β_end = 0.02, T = 1000

Cosine Schedule (Better for images):

Uses a cosine function for smoother transitions
Better preserves signal at early timesteps

Why it matters: The schedule affects:

Training stability
Generation quality
How many steps are needed for good results

3. Reverse Diffusion (Denoising)

Goal: Learn to predict the noise added at each timestep

Given noisy image x_t and timestep t:
- Neural network predicts: ε_θ(x_t, t)
- Remove predicted noise to get x_{t-1}
- Repeat until we reach x₀ (clean image)

Training objective (simplified):
L = E[||ε - ε_θ(x_t, t)||²]

We train the network to predict the noise, then subtract it!

4. DDPM (Denoising Diffusion Probabilistic Models)

Original formulation by Ho et al. (2020):

Sampling Algorithm:

Start with x_T ~ N(0, I) (random noise)

For t = T down to 1:
    1. Predict noise: ε = ε_θ(x_t, t)
    2. Compute mean: μ_t = (1/√(1-β_t)) · (x_t - (β_t/√(1-ᾱ_t)) · ε)
    3. Sample: x_{t-1} = μ_t + σ_t · z, where z ~ N(0, I)
    4. (σ_t is the variance at timestep t)

Return x₀

Key Properties:

Requires T steps (typically 1000) for high quality
Stochastic sampling (randomness at each step)
Slow but high quality

5. DDIM (Denoising Diffusion Implicit Models)

Improvement by Song et al. (2021):

Key Innovation: Deterministic sampling with fewer steps

Sampling Algorithm:

Start with x_T ~ N(0, I)

For t = T, T-skip, T-2×skip, ..., 0:
    1. Predict noise: ε = ε_θ(x_t, t)
    2. Predict x₀: x̂₀ = (x_t - √(1-ᾱ_t) · ε) / √(ᾱ_t)
    3. Compute x_{t-skip}: x_{t-skip} = √(ᾱ_{t-skip}) · x̂₀ + √(1-ᾱ_{t-skip}) · ε

Return x₀

Advantages:

Can skip steps (e.g., use 50 steps instead of 1000)
Deterministic (same noise → same image)
10-50x faster than DDPM with similar quality

6. Stable Diffusion

Modern architecture by Rombach et al. (2022):

Key Innovation: Work in latent space instead of pixel space

Architecture:

Text → CLIP Text Encoder → Text Embeddings
    ↓
Image → VAE Encoder → Latent z (compressed 8x)
    ↓
Latent Diffusion (U-Net with cross-attention to text)
    ↓
VAE Decoder → Generated Image

Benefits:
- 8x compression: 512×512 image → 64×64 latent
- Much faster and more memory-efficient
- Can condition on text, images, etc.

Components:

VAE (Variational Autoencoder): Compress images to latent space
U-Net: Predict noise in latent space (with text cross-attention)
Text Encoder: CLIP or T5 to encode text prompts
Scheduler: DDIM, DDPM, or others for sampling

Architecture Overview

File Structure

src/
├── Interfaces/
│   ├── IDiffusionModel.cs           # Main diffusion interface
│   ├── INoiseScheduler.cs           # Noise schedule interface
│   ├── ITimeEmbedding.cs            # Timestep embedding interface
│   └── IUNet.cs                     # U-Net interface
├── Models/
│   └── Generative/
│       └── Diffusion/
│           ├── DiffusionModelBase.cs      # Base diffusion model
│           ├── DDPMModel.cs               # DDPM implementation
│           ├── DDIMSampler.cs             # DDIM sampling
│           └── StableDiffusion.cs         # Stable Diffusion
├── Diffusion/
│   ├── Schedulers/
│   │   ├── NoiseScheduler.cs        # Noise schedule base
│   │   ├── LinearSchedule.cs        # Linear beta schedule
│   │   ├── CosineSchedule.cs        # Cosine schedule
│   │   └── DDIMScheduler.cs         # DDIM-specific scheduler
│   ├── UNet/
│   │   ├── UNetModel.cs             # U-Net architecture
│   │   ├── ResidualBlock.cs         # ResNet-style blocks
│   │   ├── AttentionBlock.cs        # Self-attention
│   │   ├── CrossAttentionBlock.cs   # Cross-attention (for text)
│   │   └── TimeEmbedding.cs         # Sinusoidal time embeddings
│   └── VAE/
│       ├── VAEEncoder.cs            # Image → latent
│       └── VAEDecoder.cs            # Latent → image

Class Hierarchy

IDiffusionModel<T>
    ↓ implements IGenerativeModel<T>
    ↓
DiffusionModelBase<T> (abstract)
    ├── DDPMModel<T>         # Original DDPM
    └── StableDiffusion<T>   # Latent diffusion

INoiseScheduler<T>
    ├── LinearSchedule<T>    # Linear beta schedule
    └── CosineSchedule<T>    # Cosine schedule

IUNet<T>
    └── UNetModel<T>         # U-Net with attention

Step-by-Step Implementation

Step 1: Core Interfaces

File: `src/Interfaces/INoiseScheduler.cs`

namespace AiDotNet.Interfaces;

/// <summary>
/// Represents a noise scheduler for diffusion models.
/// </summary>
/// <remarks>
/// <para><b>For Beginners:</b>
/// The noise scheduler controls how noise is added during the forward process
/// and removed during the reverse process.
///
/// Key concepts:
/// - **Beta (β_t)**: Amount of noise added at timestep t
/// - **Alpha (α_t)**: 1 - β_t (signal retained)
/// - **Alpha bar (ᾱ_t)**: Cumulative product of alphas
///
/// The scheduler pre-computes these values for efficient sampling.
/// </para>
/// </remarks>
/// <typeparam name="T">The numeric type for calculations.</typeparam>
public interface INoiseScheduler<T>
{
    /// <summary>
    /// Gets the total number of timesteps.
    /// </summary>
    int NumTimesteps { get; }

    /// <summary>
    /// Gets the beta value at a specific timestep.
    /// </summary>
    /// <param name="t">The timestep (0 to NumTimesteps-1).</param>
    /// <returns>Beta value at timestep t.</returns>
    T GetBeta(int t);

    /// <summary>
    /// Gets the alpha value at a specific timestep (α_t = 1 - β_t).
    /// </summary>
    T GetAlpha(int t);

    /// <summary>
    /// Gets the cumulative alpha product at a specific timestep.
    /// ᾱ_t = ∏(α_s) for s=0 to t
    /// </summary>
    T GetAlphaBar(int t);

    /// <summary>
    /// Adds noise to a clean sample at a given timestep.
    /// x_t = √(ᾱ_t) · x₀ + √(1 - ᾱ_t) · ε
    /// </summary>
    /// <param name="x0">Clean sample.</param>
    /// <param name="noise">Random Gaussian noise.</param>
    /// <param name="t">Timestep.</param>
    /// <param name="ops">Numeric operations provider.</param>
    /// <returns>Noisy sample at timestep t.</returns>
    Tensor<T> AddNoise(Tensor<T> x0, Tensor<T> noise, int t, INumericOperations<T> ops);

    /// <summary>
    /// Removes noise from a sample (one denoising step).
    /// </summary>
    /// <param name="xt">Noisy sample at timestep t.</param>
    /// <param name="predictedNoise">Noise predicted by the model.</param>
    /// <param name="t">Current timestep.</param>
    /// <param name="ops">Numeric operations provider.</param>
    /// <returns>Denoised sample at timestep t-1.</returns>
    Tensor<T> RemoveNoise(
        Tensor<T> xt,
        Tensor<T> predictedNoise,
        int t,
        INumericOperations<T> ops);
}

File: `src/Interfaces/IDiffusionModel.cs`

namespace AiDotNet.Interfaces;

/// <summary>
/// Represents a diffusion model for image generation.
/// </summary>
/// <remarks>
/// <para><b>For Beginners:</b>
/// Diffusion models generate images by:
/// 1. Starting with random noise
/// 2. Gradually removing noise over many steps
/// 3. Using a neural network to predict the noise at each step
///
/// The model can be:
/// - **Unconditional**: Generate random images from the training distribution
/// - **Conditional**: Generate images based on text, class labels, or other inputs
/// </para>
/// </remarks>
/// <typeparam name="T">The numeric type for calculations.</typeparam>
public interface IDiffusionModel<T> : IGenerativeModel<T>
{
    /// <summary>
    /// Gets the noise scheduler.
    /// </summary>
    INoiseScheduler<T> Scheduler { get; }

    /// <summary>
    /// Gets the number of diffusion timesteps.
    /// </summary>
    int NumTimesteps { get; }

    /// <summary>
    /// Predicts the noise in a noisy sample at a given timestep.
    /// </summary>
    /// <param name="xt">Noisy sample at timestep t.</param>
    /// <param name="t">Timestep (0 to NumTimesteps-1).</param>
    /// <param name="condition">Optional conditioning (text embeddings, class labels, etc.).</param>
    /// <returns>Predicted noise tensor.</returns>
    Tensor<T> PredictNoise(Tensor<T> xt, int t, Tensor<T>? condition = null);

    /// <summary>
    /// Performs one denoising step.
    /// </summary>
    /// <param name="xt">Noisy sample at timestep t.</param>
    /// <param name="t">Current timestep.</param>
    /// <param name="condition">Optional conditioning.</param>
    /// <returns>Less noisy sample at timestep t-1.</returns>
    Tensor<T> DenoisingStep(Tensor<T> xt, int t, Tensor<T>? condition = null);

    /// <summary>
    /// Generates samples from random noise.
    /// </summary>
    /// <param name="shape">Shape of samples to generate [batch, channels, height, width].</param>
    /// <param name="condition">Optional conditioning.</param>
    /// <param name="numInferenceSteps">Number of denoising steps (can be less than NumTimesteps).</param>
    /// <returns>Generated samples.</returns>
    Tensor<T> Sample(int[] shape, Tensor<T>? condition = null, int? numInferenceSteps = null);

    /// <summary>
    /// Trains the diffusion model on a batch of images.
    /// </summary>
    /// <param name="images">Training images.</param>
    /// <param name="condition">Optional conditioning for conditional generation.</param>
    /// <returns>Training loss.</returns>
    T TrainStep(Tensor<T> images, Tensor<T>? condition = null);
}

Step 2: Noise Schedulers

File: `src/Diffusion/Schedulers/NoiseScheduler.cs`

namespace AiDotNet.Diffusion.Schedulers;

using AiDotNet.Interfaces;
using AiDotNet.Mathematics;
using AiDotNet.Validation;

/// <summary>
/// Base class for noise schedulers in diffusion models.
/// </summary>
/// <typeparam name="T">The numeric type for calculations.</typeparam>
public abstract class NoiseScheduler<T> : INoiseScheduler<T>
{
    protected readonly Vector<T> _betas;
    protected readonly Vector<T> _alphas;
    protected readonly Vector<T> _alphaBars;
    protected readonly Vector<T> _sqrtAlphaBars;
    protected readonly Vector<T> _sqrtOneMinusAlphaBars;
    protected readonly int _numTimesteps;
    protected readonly INumericOperations<T> _ops;

    /// <summary>
    /// Initializes a new instance of the <see cref="NoiseScheduler{T}"/> class.
    /// </summary>
    /// <param name="numTimesteps">Total number of diffusion timesteps.</param>
    /// <param name="ops">Numeric operations provider.</param>
    protected NoiseScheduler(int numTimesteps, INumericOperations<T> ops)
    {
        Guard.Positive(numTimesteps, nameof(numTimesteps));
        Guard.NotNull(ops, nameof(ops));

        _numTimesteps = numTimesteps;
        _ops = ops;

        _betas = new Vector<T>(numTimesteps);
        _alphas = new Vector<T>(numTimesteps);
        _alphaBars = new Vector<T>(numTimesteps);
        _sqrtAlphaBars = new Vector<T>(numTimesteps);
        _sqrtOneMinusAlphaBars = new Vector<T>(numTimesteps);

        InitializeSchedule();
        ComputeDerivedValues();
    }

    /// <inheritdoc/>
    public int NumTimesteps => _numTimesteps;

    /// <inheritdoc/>
    public T GetBeta(int t)
    {
        Guard.InRange(t, 0, _numTimesteps - 1, nameof(t));
        return _betas[t];
    }

    /// <inheritdoc/>
    public T GetAlpha(int t)
    {
        Guard.InRange(t, 0, _numTimesteps - 1, nameof(t));
        return _alphas[t];
    }

    /// <inheritdoc/>
    public T GetAlphaBar(int t)
    {
        Guard.InRange(t, 0, _numTimesteps - 1, nameof(t));
        return _alphaBars[t];
    }

    /// <inheritdoc/>
    public Tensor<T> AddNoise(
        Tensor<T> x0,
        Tensor<T> noise,
        int t,
        INumericOperations<T> ops)
    {
        Guard.NotNull(x0, nameof(x0));
        Guard.NotNull(noise, nameof(noise));
        Guard.NotNull(ops, nameof(ops));
        Guard.InRange(t, 0, _numTimesteps - 1, nameof(t));

        if (!x0.Shape.SequenceEqual(noise.Shape))
        {
            throw new ArgumentException(
                $"x0 and noise must have the same shape. Got x0: [{string.Join(", ", x0.Shape)}], noise: [{string.Join(", ", noise.Shape)}]",
                nameof(noise));
        }

        // x_t = √(ᾱ_t) · x₀ + √(1 - ᾱ_t) · ε
        var sqrtAlphaBar = _sqrtAlphaBars[t];
        var sqrtOneMinusAlphaBar = _sqrtOneMinusAlphaBars[t];

        var result = new Tensor<T>(x0.Shape);
        for (int i = 0; i < x0.Data.Length; i++)
        {
            var signalPart = ops.Multiply(sqrtAlphaBar, x0.Data[i]);
            var noisePart = ops.Multiply(sqrtOneMinusAlphaBar, noise.Data[i]);
            result.Data[i] = ops.Add(signalPart, noisePart);
        }

        return result;
    }

    /// <inheritdoc/>
    public abstract Tensor<T> RemoveNoise(
        Tensor<T> xt,
        Tensor<T> predictedNoise,
        int t,
        INumericOperations<T> ops);

    /// <summary>
    /// Initializes the beta schedule. Must be implemented by subclasses.
    /// </summary>
    protected abstract void InitializeSchedule();

    /// <summary>
    /// Computes derived values (alphas, alpha_bars, etc.) from betas.
    /// </summary>
    private void ComputeDerivedValues()
    {
        // α_t = 1 - β_t
        for (int t = 0; t < _numTimesteps; t++)
        {
            _alphas[t] = _ops.Subtract(_ops.One, _betas[t]);
        }

        // ᾱ_t = ∏(α_s) for s=0 to t
        T cumulativeProduct = _ops.One;
        for (int t = 0; t < _numTimesteps; t++)
        {
            cumulativeProduct = _ops.Multiply(cumulativeProduct, _alphas[t]);
            _alphaBars[t] = cumulativeProduct;
        }

        // Pre-compute square roots for efficiency
        for (int t = 0; t < _numTimesteps; t++)
        {
            _sqrtAlphaBars[t] = _ops.Sqrt(_alphaBars[t]);
            var oneMinusAlphaBar = _ops.Subtract(_ops.One, _alphaBars[t]);
            _sqrtOneMinusAlphaBars[t] = _ops.Sqrt(oneMinusAlphaBar);
        }
    }
}

File: `src/Diffusion/Schedulers/LinearSchedule.cs`

namespace AiDotNet.Diffusion.Schedulers;

using AiDotNet.Interfaces;
using AiDotNet.Mathematics;
using AiDotNet.Validation;

/// <summary>
/// Implements a linear noise schedule for diffusion models.
/// </summary>
/// <remarks>
/// <para><b>For Beginners:</b>
/// Linear schedule increases noise uniformly from β_start to β_end.
///
/// Example: With β_start = 0.0001 and β_end = 0.02:
/// - At t=0: very little noise added (β = 0.0001)
/// - At t=T/2: medium noise (β ≈ 0.01)
/// - At t=T: maximum noise (β = 0.02)
///
/// This was used in the original DDPM paper.
/// </para>
/// </remarks>
/// <typeparam name="T">The numeric type for calculations.</typeparam>
public class LinearSchedule<T> : NoiseScheduler<T>
{
    private readonly double _betaStart;
    private readonly double _betaEnd;

    /// <summary>
    /// Initializes a new instance of the <see cref="LinearSchedule{T}"/> class.
    /// </summary>
    /// <param name="numTimesteps">Total number of timesteps.</param>
    /// <param name="betaStart">Starting beta value (e.g., 0.0001).</param>
    /// <param name="betaEnd">Ending beta value (e.g., 0.02).</param>
    /// <param name="ops">Numeric operations provider.</param>
    public LinearSchedule(
        int numTimesteps,
        double betaStart,
        double betaEnd,
        INumericOperations<T> ops)
        : base(numTimesteps, ops)
    {
        Guard.Positive(betaStart, nameof(betaStart));
        Guard.Positive(betaEnd, nameof(betaEnd));

        if (betaStart >= betaEnd)
        {
            throw new ArgumentException(
                $"betaStart ({betaStart}) must be less than betaEnd ({betaEnd})",
                nameof(betaStart));
        }

        _betaStart = betaStart;
        _betaEnd = betaEnd;
    }

    /// <inheritdoc/>
    protected override void InitializeSchedule()
    {
        // Linear interpolation from betaStart to betaEnd
        for (int t = 0; t < _numTimesteps; t++)
        {
            double fraction = (double)t / (_numTimesteps - 1);
            double beta = _betaStart + fraction * (_betaEnd - _betaStart);
            _betas[t] = _ops.FromDouble(beta);
        }
    }

    /// <inheritdoc/>
    public override Tensor<T> RemoveNoise(
        Tensor<T> xt,
        Tensor<T> predictedNoise,
        int t,
        INumericOperations<T> ops)
    {
        Guard.NotNull(xt, nameof(xt));
        Guard.NotNull(predictedNoise, nameof(predictedNoise));
        Guard.NotNull(ops, nameof(ops));
        Guard.InRange(t, 0, _numTimesteps - 1, nameof(t));

        // DDPM sampling formula:
        // μ_t = (1/√(α_t)) · (x_t - (β_t/√(1-ᾱ_t)) · ε_θ(x_t, t))
        // x_{t-1} = μ_t + σ_t · z, where z ~ N(0, I)

        var beta = _betas[t];
        var alpha = _alphas[t];
        var alphaBar = _alphaBars[t];
        var sqrtOneMinusAlphaBar = _sqrtOneMinusAlphaBars[t];

        // Compute mean
        var result = new Tensor<T>(xt.Shape);
        var sqrtAlpha = ops.Sqrt(alpha);
        var coeff = ops.Divide(beta, sqrtOneMinusAlphaBar);

        for (int i = 0; i < xt.Data.Length; i++)
        {
            var noiseTerm = ops.Multiply(coeff, predictedNoise.Data[i]);
            var mean = ops.Subtract(xt.Data[i], noiseTerm);
            mean = ops.Divide(mean, sqrtAlpha);

            // Add variance if not at the last step
            if (t > 0)
            {
                // Compute variance: σ_t² = β_t
                var sigma = ops.Sqrt(beta);
                var random = new Random();
                var z = SampleGaussian(random);
                var noise = ops.Multiply(sigma, ops.FromDouble(z));
                result.Data[i] = ops.Add(mean, noise);
            }
            else
            {
                result.Data[i] = mean;
            }
        }

        return result;
    }

    private static double SampleGaussian(Random random)
    {
        // Box-Muller transform
        double u1 = 1.0 - random.NextDouble();
        double u2 = 1.0 - random.NextDouble();
        return Math.Sqrt(-2.0 * Math.Log(u1)) * Math.Cos(2.0 * Math.PI * u2);
    }
}

Step 3: Time Embeddings

File: `src/Diffusion/UNet/TimeEmbedding.cs`

namespace AiDotNet.Diffusion.UNet;

using AiDotNet.Interfaces;
using AiDotNet.Mathematics;
using AiDotNet.Validation;

/// <summary>
/// Implements sinusoidal time embeddings for diffusion models.
/// </summary>
/// <remarks>
/// <para><b>For Beginners:</b>
/// Time embeddings tell the U-Net what timestep it's processing.
///
/// Why we need them:
/// - Different timesteps require different denoising strategies
/// - At t=1000 (pure noise): need aggressive denoising
/// - At t=10 (almost clean): need gentle refinement
///
/// Sinusoidal embeddings:
/// - Use sine and cosine functions of different frequencies
/// - Similar to positional encodings in transformers
/// - Allow the model to interpolate between timesteps
///
/// Example: For timestep t=500 and embedding dimension 256:
/// - pos_enc[0] = sin(500 / 10000^(0/128))
/// - pos_enc[1] = cos(500 / 10000^(0/128))
/// - pos_enc[2] = sin(500 / 10000^(2/128))
/// - ... and so on
/// </para>
/// </remarks>
/// <typeparam name="T">The numeric type for calculations.</typeparam>
public class TimeEmbedding<T>
{
    private readonly int _embedDim;
    private readonly int _maxPeriod;
    private readonly Matrix<T> _mlpWeights1;
    private readonly Vector<T> _mlpBias1;
    private readonly Matrix<T> _mlpWeights2;
    private readonly Vector<T> _mlpBias2;

    /// <summary>
    /// Initializes a new instance of the <see cref="TimeEmbedding{T}"/> class.
    /// </summary>
    /// <param name="embedDim">Dimension of the time embedding.</param>
    /// <param name="mlpDim">Hidden dimension of the MLP (typically 4 × embed_dim).</param>
    /// <param name="maxPeriod">Maximum period for sinusoidal encoding (default: 10000).</param>
    /// <param name="ops">Numeric operations provider.</param>
    public TimeEmbedding(int embedDim, int mlpDim, int maxPeriod, INumericOperations<T> ops)
    {
        Guard.Positive(embedDim, nameof(embedDim));
        Guard.Positive(mlpDim, nameof(mlpDim));
        Guard.Positive(maxPeriod, nameof(maxPeriod));
        Guard.NotNull(ops, nameof(ops));

        if (embedDim % 2 != 0)
        {
            throw new ArgumentException(
                $"Embedding dimension must be even, got {embedDim}",
                nameof(embedDim));
        }

        _embedDim = embedDim;
        _maxPeriod = maxPeriod;

        // MLP to transform sinusoidal embeddings
        _mlpWeights1 = new Matrix<T>(mlpDim, embedDim);
        _mlpBias1 = new Vector<T>(mlpDim);
        _mlpWeights2 = new Matrix<T>(embedDim, mlpDim);
        _mlpBias2 = new Vector<T>(embedDim);

        InitializeWeights(ops);
    }

    /// <summary>
    /// Gets the embedding dimension.
    /// </summary>
    public int EmbedDim => _embedDim;

    /// <summary>
    /// Computes time embeddings for a batch of timesteps.
    /// </summary>
    /// <param name="timesteps">Timesteps to embed [batch_size].</param>
    /// <param name="ops">Numeric operations provider.</param>
    /// <returns>Time embeddings [batch_size, embed_dim].</returns>
    public Tensor<T> Forward(int[] timesteps, INumericOperations<T> ops)
    {
        Guard.NotNull(timesteps, nameof(timesteps));
        Guard.NotNull(ops, nameof(ops));

        int batchSize = timesteps.Length;

        // Compute sinusoidal embeddings
        var sinusoidalEmbeds = new Tensor<T>(new[] { batchSize, _embedDim });

        for (int b = 0; b < batchSize; b++)
        {
            int t = timesteps[b];
            var embedding = ComputeSinusoidalEmbedding(t, ops);

            for (int i = 0; i < _embedDim; i++)
            {
                sinusoidalEmbeds[b, i] = embedding[i];
            }
        }

        // Apply MLP: Linear → SiLU → Linear
        var hidden = ApplyLinear(sinusoidalEmbeds, _mlpWeights1, _mlpBias1, ops);
        hidden = ApplySiLU(hidden, ops);
        var output = ApplyLinear(hidden, _mlpWeights2, _mlpBias2, ops);

        return output;
    }

    private Vector<T> ComputeSinusoidalEmbedding(int timestep, INumericOperations<T> ops)
    {
        var embedding = new Vector<T>(_embedDim);
        int halfDim = _embedDim / 2;

        // Compute frequencies: 1 / (max_period ^ (2i / embed_dim))
        for (int i = 0; i < halfDim; i++)
        {
            double exponent = -Math.Log(_maxPeriod) * (2.0 * i) / _embedDim;
            double freq = Math.Exp(exponent);

            // Sine component
            embedding[i] = ops.FromDouble(Math.Sin(timestep * freq));

            // Cosine component
            embedding[halfDim + i] = ops.FromDouble(Math.Cos(timestep * freq));
        }

        return embedding;
    }

    private Tensor<T> ApplyLinear(
        Tensor<T> input,
        Matrix<T> weights,
        Vector<T> bias,
        INumericOperations<T> ops)
    {
        // input: [batch, in_features]
        // weights: [out_features, in_features]
        // output: [batch, out_features]

        var shape = input.Shape;
        int batch = shape[0];
        int inFeatures = shape[1];
        int outFeatures = weights.Rows;

        var output = new Tensor<T>(new[] { batch, outFeatures });

        for (int b = 0; b < batch; b++)
        {
            for (int o = 0; o < outFeatures; o++)
            {
                T sum = bias[o];
                for (int i = 0; i < inFeatures; i++)
                {
                    var prod = ops.Multiply(input[b, i], weights[o, i]);
                    sum = ops.Add(sum, prod);
                }
                output[b, o] = sum;
            }
        }

        return output;
    }

    private Tensor<T> ApplySiLU(Tensor<T> input, INumericOperations<T> ops)
    {
        // SiLU (Swish): x * sigmoid(x)
        var output = new Tensor<T>(input.Shape);

        for (int i = 0; i < input.Data.Length; i++)
        {
            var x = input.Data[i];
            // sigmoid(x) = 1 / (1 + e^(-x))
            var negX = ops.Negate(x);
            var expNegX = ops.Exp(negX);
            var sigmoid = ops.Divide(ops.One, ops.Add(ops.One, expNegX));
            output.Data[i] = ops.Multiply(x, sigmoid);
        }

        return output;
    }

    private void InitializeWeights(INumericOperations<T> ops)
    {
        var random = new Random(42);

        // Xavier initialization for MLP weights
        double stddev1 = Math.Sqrt(2.0 / (_embedDim + _mlpWeights1.Rows));
        InitializeMatrix(_mlpWeights1, random, stddev1, ops);

        double stddev2 = Math.Sqrt(2.0 / (_mlpWeights1.Rows + _embedDim));
        InitializeMatrix(_mlpWeights2, random, stddev2, ops);

        // Zero bias
        for (int i = 0; i < _mlpBias1.Length; i++)
        {
            _mlpBias1[i] = ops.Zero;
        }

        for (int i = 0; i < _mlpBias2.Length; i++)
        {
            _mlpBias2[i] = ops.Zero;
        }
    }

    private void InitializeMatrix(
        Matrix<T> matrix,
        Random random,
        double stddev,
        INumericOperations<T> ops)
    {
        for (int i = 0; i < matrix.Rows; i++)
        {
            for (int j = 0; j < matrix.Columns; j++)
            {
                double u1 = 1.0 - random.NextDouble();
                double u2 = 1.0 - random.NextDouble();
                double z0 = Math.Sqrt(-2.0 * Math.Log(u1)) * Math.Cos(2.0 * Math.PI * u2);
                matrix[i, j] = ops.FromDouble(stddev * z0);
            }
        }
    }
}

Step 4: U-Net Architecture (Simplified)

File: `src/Interfaces/IUNet.cs`

namespace AiDotNet.Interfaces;

/// <summary>
/// Represents a U-Net architecture for diffusion models.
/// </summary>
/// <remarks>
/// <para><b>For Beginners:</b>
/// U-Net is a neural network shaped like the letter "U":
///
/// Structure:
/// ```
/// Input → Encoder (downsampling) → Bottleneck → Decoder (upsampling) → Output
///         ↓                                           ↑
///         Skip connections ────────────────────────────
/// ```
///
/// Why U-Net for diffusion:
/// - **Encoder**: Compress image to capture semantic information
/// - **Bottleneck**: Process at lowest resolution with attention
/// - **Decoder**: Reconstruct details with help from skip connections
/// - **Skip connections**: Preserve fine details from encoder
///
/// For diffusion, U-Net predicts the noise added to the image.
/// </para>
/// </remarks>
/// <typeparam name="T">The numeric type for calculations.</typeparam>
public interface IUNet<T>
{
    /// <summary>
    /// Predicts noise in a noisy image at a given timestep.
    /// </summary>
    /// <param name="noisyImage">Noisy image [batch, channels, height, width].</param>
    /// <param name="timestep">Timestep(s) [batch] or single value.</param>
    /// <param name="condition">Optional conditioning (text embeddings, class labels, etc.).</param>
    /// <param name="ops">Numeric operations provider.</param>
    /// <returns>Predicted noise [batch, channels, height, width].</returns>
    Tensor<T> Forward(
        Tensor<T> noisyImage,
        int[] timestep,
        Tensor<T>? condition,
        INumericOperations<T> ops);

    /// <summary>
    /// Gets the input channels.
    /// </summary>
    int InChannels { get; }

    /// <summary>
    /// Gets the output channels.
    /// </summary>
    int OutChannels { get; }

    /// <summary>
    /// Gets the base number of channels (increases with depth).
    /// </summary>
    int BaseChannels { get; }

    /// <summary>
    /// Gets the number of downsampling/upsampling stages.
    /// </summary>
    int NumLevels { get; }
}

Step 5: DDPM Model

File: `src/Models/Generative/Diffusion/DDPMModel.cs`

namespace AiDotNet.Models.Generative.Diffusion;

using AiDotNet.Interfaces;
using AiDotNet.Diffusion.Schedulers;
using AiDotNet.Mathematics;
using AiDotNet.Validation;

/// <summary>
/// Implements the Denoising Diffusion Probabilistic Model (DDPM).
/// </summary>
/// <remarks>
/// <para><b>Paper</b>: "Denoising Diffusion Probabilistic Models"
/// by Ho et al. (NeurIPS 2020)
///
/// <b>Key Contributions</b>:
/// 1. Simplified training objective: predict noise instead of x₀
/// 2. Linear or cosine noise schedule
/// 3. High-quality image generation with simple architecture
///
/// <b>Training Process</b>:
/// 1. Sample a clean image x₀ from training data
/// 2. Sample timestep t uniformly from [0, T]
/// 3. Sample noise ε ~ N(0, I)
/// 4. Create noisy image: x_t = √(ᾱ_t)·x₀ + √(1-ᾱ_t)·ε
/// 5. Predict noise: ε_θ(x_t, t)
/// 6. Compute loss: L = ||ε - ε_θ(x_t, t)||²
/// 7. Update model parameters
///
/// <b>Sampling Process</b>:
/// 1. Start with x_T ~ N(0, I) (random noise)
/// 2. For t = T down to 1:
///    - Predict noise: ε = ε_θ(x_t, t)
///    - Compute mean: μ_t (see scheduler)
///    - Sample: x_{t-1} = μ_t + σ_t·z
/// 3. Return x₀
///
/// <b>For Beginners</b>:
/// DDPM showed that diffusion models can generate high-quality images
/// by learning to reverse a gradual noising process. The key insight is
/// that predicting noise is easier than predicting the clean image directly.
/// </para>
/// </remarks>
/// <typeparam name="T">The numeric type for calculations.</typeparam>
public class DDPMModel<T> : IDiffusionModel<T>
{
    private readonly IUNet<T> _unet;
    private readonly INoiseScheduler<T> _scheduler;
    private readonly INumericOperations<T> _ops;
    private readonly int _imageSize;
    private readonly int _channels;

    /// <summary>
    /// Initializes a new instance of the <see cref="DDPMModel{T}"/> class.
    /// </summary>
    /// <param name="unet">The U-Net architecture for noise prediction.</param>
    /// <param name="scheduler">The noise scheduler.</param>
    /// <param name="imageSize">Size of images (assumed square).</param>
    /// <param name="channels">Number of image channels (e.g., 3 for RGB).</param>
    /// <param name="ops">Numeric operations provider.</param>
    public DDPMModel(
        IUNet<T> unet,
        INoiseScheduler<T> scheduler,
        int imageSize,
        int channels,
        INumericOperations<T> ops)
    {
        Guard.NotNull(unet, nameof(unet));
        Guard.NotNull(scheduler, nameof(scheduler));
        Guard.Positive(imageSize, nameof(imageSize));
        Guard.Positive(channels, nameof(channels));
        Guard.NotNull(ops, nameof(ops));

        _unet = unet;
        _scheduler = scheduler;
        _imageSize = imageSize;
        _channels = channels;
        _ops = ops;
    }

    /// <inheritdoc/>
    public INoiseScheduler<T> Scheduler => _scheduler;

    /// <inheritdoc/>
    public int NumTimesteps => _scheduler.NumTimesteps;

    /// <inheritdoc/>
    public Tensor<T> PredictNoise(Tensor<T> xt, int t, Tensor<T>? condition = null)
    {
        Guard.NotNull(xt, nameof(xt));
        Guard.InRange(t, 0, NumTimesteps - 1, nameof(t));

        // Get batch size from input
        int batch = xt.Shape[0];

        // Create timestep array (same timestep for all samples in batch)
        var timesteps = new int[batch];
        for (int i = 0; i < batch; i++)
        {
            timesteps[i] = t;
        }

        // Predict noise using U-Net
        return _unet.Forward(xt, timesteps, condition, _ops);
    }

    /// <inheritdoc/>
    public Tensor<T> DenoisingStep(Tensor<T> xt, int t, Tensor<T>? condition = null)
    {
        Guard.NotNull(xt, nameof(xt));
        Guard.InRange(t, 0, NumTimesteps - 1, nameof(t));

        // Predict noise
        var predictedNoise = PredictNoise(xt, t, condition);

        // Remove noise using scheduler
        return _scheduler.RemoveNoise(xt, predictedNoise, t, _ops);
    }

    /// <inheritdoc/>
    public Tensor<T> Sample(int[] shape, Tensor<T>? condition = null, int? numInferenceSteps = null)
    {
        Guard.NotNull(shape, nameof(shape));

        if (shape.Length != 4)
        {
            throw new ArgumentException(
                $"Shape must be 4D [batch, channels, height, width], got: [{string.Join(", ", shape)}]",
                nameof(shape));
        }

        int batch = shape[0];
        int channels = shape[1];
        int height = shape[2];
        int width = shape[3];

        if (channels != _channels || height != _imageSize || width != _imageSize)
        {
            throw new ArgumentException(
                $"Expected shape [*, {_channels}, {_imageSize}, {_imageSize}], got: [{string.Join(", ", shape)}]",
                nameof(shape));
        }

        // Start with random Gaussian noise
        var xt = SampleGaussianNoise(shape);

        // Determine number of steps
        int steps = numInferenceSteps ?? NumTimesteps;

        // Denoising loop
        for (int t = NumTimesteps - 1; t >= 0; t--)
        {
            xt = DenoisingStep(xt, t, condition);

            // Optional: Log progress
            if (t % 100 == 0)
            {
                Console.WriteLine($"Denoising step {NumTimesteps - t}/{NumTimesteps}");
            }
        }

        return xt;
    }

    /// <inheritdoc/>
    public T TrainStep(Tensor<T> images, Tensor<T>? condition = null)
    {
        Guard.NotNull(images, nameof(images));

        var shape = images.Shape;
        if (shape.Length != 4)
        {
            throw new ArgumentException(
                $"Images must be 4D [batch, channels, height, width], got: [{string.Join(", ", shape)}]",
                nameof(images));
        }

        int batch = shape[0];

        // Sample random timesteps for each image in the batch
        var random = new Random();
        var timesteps = new int[batch];
        for (int i = 0; i < batch; i++)
        {
            timesteps[i] = random.Next(NumTimesteps);
        }

        // Sample Gaussian noise
        var noise = SampleGaussianNoise(shape);

        // Add noise to images
        var noisyImages = new Tensor<T>(shape);
        for (int b = 0; b < batch; b++)
        {
            int t = timesteps[b];

            // Extract single image and noise
            var image = ExtractSample(images, b);
            var noiseForImage = ExtractSample(noise, b);

            // Add noise at timestep t
            var noisyImage = _scheduler.AddNoise(image, noiseForImage, t, _ops);

            // Copy back to batch
            CopySampleToBatch(noisyImage, noisyImages, b);
        }

        // Predict noise
        var predictedNoise = _unet.Forward(noisyImages, timesteps, condition, _ops);

        // Compute mean squared error loss
        var loss = ComputeMSELoss(noise, predictedNoise);

        // TODO: Backpropagate and update weights
        // This requires implementing:
        // 1. Gradient computation through U-Net
        // 2. Optimizer (Adam/AdamW)
        // 3. Parameter updates

        return loss;
    }

    private Tensor<T> SampleGaussianNoise(int[] shape)
    {
        var noise = new Tensor<T>(shape);
        var random = new Random();

        for (int i = 0; i < noise.Data.Length; i++)
        {
            // Box-Muller transform for Gaussian samples
            double u1 = 1.0 - random.NextDouble();
            double u2 = 1.0 - random.NextDouble();
            double z = Math.Sqrt(-2.0 * Math.Log(u1)) * Math.Cos(2.0 * Math.PI * u2);
            noise.Data[i] = _ops.FromDouble(z);
        }

        return noise;
    }

    private Tensor<T> ExtractSample(Tensor<T> batch, int index)
    {
        // Extract sample at index from [batch, channels, height, width]
        int channels = batch.Shape[1];
        int height = batch.Shape[2];
        int width = batch.Shape[3];

        var sample = new Tensor<T>(new[] { 1, channels, height, width });

        for (int c = 0; c < channels; c++)
        {
            for (int h = 0; h < height; h++)
            {
                for (int w = 0; w < width; w++)
                {
                    sample[0, c, h, w] = batch[index, c, h, w];
                }
            }
        }

        return sample;
    }

    private void CopySampleToBatch(Tensor<T> sample, Tensor<T> batch, int index)
    {
        int channels = sample.Shape[1];
        int height = sample.Shape[2];
        int width = sample.Shape[3];

        for (int c = 0; c < channels; c++)
        {
            for (int h = 0; h < height; h++)
            {
                for (int w = 0; w < width; w++)
                {
                    batch[index, c, h, w] = sample[0, c, h, w];
                }
            }
        }
    }

    private T ComputeMSELoss(Tensor<T> target, Tensor<T> prediction)
    {
        // Mean Squared Error: (1/N) * sum((target - prediction)²)
        T sumSquaredError = _ops.Zero;
        int count = target.Data.Length;

        for (int i = 0; i < count; i++)
        {
            var diff = _ops.Subtract(target.Data[i], prediction.Data[i]);
            var squared = _ops.Square(diff);
            sumSquaredError = _ops.Add(sumSquaredError, squared);
        }

        return _ops.Divide(sumSquaredError, _ops.FromDouble(count));
    }

    /// <inheritdoc/>
    public void Save(string path)
    {
        Guard.NotNullOrEmpty(path, nameof(path));

        // TODO: Implement model serialization
        // Save U-Net weights, scheduler configuration, etc.
    }

    /// <inheritdoc/>
    public void Load(string path)
    {
        Guard.NotNullOrEmpty(path, nameof(path));

        // TODO: Implement model deserialization
    }

    /// <inheritdoc/>
    public Tensor<T> Generate(int numSamples)
    {
        var shape = new[] { numSamples, _channels, _imageSize, _imageSize };
        return Sample(shape);
    }
}

Testing Strategy

Unit Tests

namespace AiDotNetTests.UnitTests.Diffusion;

using AiDotNet.Diffusion.Schedulers;
using AiDotNet.Mathematics;
using Xunit;

public class NoiseSchedulerTests
{
    [Fact]
    public void LinearSchedule_ComputesCorrectBetas()
    {
        // Arrange
        var ops = new DoubleNumericOperations();
        var scheduler = new LinearSchedule<double>(1000, 0.0001, 0.02, ops);

        // Act
        var betaStart = scheduler.GetBeta(0);
        var betaEnd = scheduler.GetBeta(999);

        // Assert
        Assert.True(Math.Abs(betaStart - 0.0001) < 0.00001);
        Assert.True(Math.Abs(betaEnd - 0.02) < 0.00001);
    }

    [Fact]
    public void AddNoise_PreservesShape()
    {
        // Arrange
        var ops = new DoubleNumericOperations();
        var scheduler = new LinearSchedule<double>(1000, 0.0001, 0.02, ops);

        var x0 = new Tensor<double>(new[] { 2, 3, 32, 32 });
        var noise = new Tensor<double>(new[] { 2, 3, 32, 32 });

        // Act
        var xt = scheduler.AddNoise(x0, noise, 500, ops);

        // Assert
        Assert.Equal(new[] { 2, 3, 32, 32 }, xt.Shape);
    }

    [Fact]
    public void AddNoise_AtT0_ReturnsOriginal()
    {
        // Arrange
        var ops = new DoubleNumericOperations();
        var scheduler = new LinearSchedule<double>(1000, 0.0001, 0.02, ops);

        var x0 = new Tensor<double>(new[] { 1, 3, 4, 4 });
        for (int i = 0; i < x0.Data.Length; i++)
        {
            x0.Data[i] = i + 1.0; // Fill with sequential values
        }

        var noise = new Tensor<double>(new[] { 1, 3, 4, 4 });
        // noise is all zeros

        // Act
        var xt = scheduler.AddNoise(x0, noise, 0, ops);

        // Assert - Should be very close to x0 (alpha_bar_0 ≈ 1)
        for (int i = 0; i < x0.Data.Length; i++)
        {
            Assert.True(Math.Abs(xt.Data[i] - x0.Data[i]) < 0.01);
        }
    }
}

public class TimeEmbeddingTests
{
    [Fact]
    public void Forward_ReturnsCorrectShape()
    {
        // Arrange
        var ops = new DoubleNumericOperations();
        var timeEmbed = new TimeEmbedding<double>(256, 1024, 10000, ops);

        var timesteps = new[] { 0, 100, 500, 999 };

        // Act
        var embeddings = timeEmbed.Forward(timesteps, ops);

        // Assert
        Assert.Equal(new[] { 4, 256 }, embeddings.Shape);
    }

    [Fact]
    public void Forward_DifferentTimestepsProduceDifferentEmbeddings()
    {
        // Arrange
        var ops = new DoubleNumericOperations();
        var timeEmbed = new TimeEmbedding<double>(256, 1024, 10000, ops);

        // Act
        var embed1 = timeEmbed.Forward(new[] { 0 }, ops);
        var embed2 = timeEmbed.Forward(new[] { 500 }, ops);

        // Assert - Embeddings should be different
        bool different = false;
        for (int i = 0; i < 256; i++)
        {
            if (Math.Abs(embed1[0, i] - embed2[0, i]) > 0.01)
            {
                different = true;
                break;
            }
        }
        Assert.True(different);
    }
}

public class DDPMModelTests
{
    [Fact]
    public void Sample_GeneratesCorrectShape()
    {
        // Arrange
        var ops = new DoubleNumericOperations();
        var scheduler = new LinearSchedule<double>(100, 0.0001, 0.02, ops); // Small T for testing

        // Create mock U-Net (returns zeros for simplicity)
        var unet = new MockUNet<double>(3, 3, 64, 4);

        var model = new DDPMModel<double>(unet, scheduler, 32, 3, ops);

        // Act
        var samples = model.Sample(new[] { 2, 3, 32, 32 });

        // Assert
        Assert.Equal(new[] { 2, 3, 32, 32 }, samples.Shape);
    }

    [Fact]
    public void TrainStep_ComputesLoss()
    {
        // Arrange
        var ops = new DoubleNumericOperations();
        var scheduler = new LinearSchedule<double>(1000, 0.0001, 0.02, ops);
        var unet = new MockUNet<double>(3, 3, 64, 4);
        var model = new DDPMModel<double>(unet, scheduler, 32, 3, ops);

        var images = new Tensor<double>(new[] { 4, 3, 32, 32 });

        // Act
        var loss = model.TrainStep(images);

        // Assert
        Assert.True(loss >= 0); // Loss should be non-negative
    }
}

Training Strategy

DDPM Training

/// <summary>
/// Trains a DDPM model on an image dataset.
/// </summary>
/// <remarks>
/// <b>Training Hyperparameters</b> (from original paper):
///
/// 1. **Optimizer**: Adam with β₁=0.9, β₂=0.999
/// 2. **Learning Rate**: 2 × 10⁻⁴ (constant)
/// 3. **Batch Size**: 128
/// 4. **Training Steps**: 800K steps
/// 5. **EMA**: Exponential Moving Average with decay 0.9999
/// 6. **Image Size**: 32×32 (CIFAR-10) or 256×256 (CelebA-HQ)
///
/// <b>Data Augmentation</b>:
/// - Random horizontal flips
/// - No other augmentation (diffusion provides implicit regularization)
///
/// <b>Training Loop</b>:
/// ```
/// for each batch:
///     1. Sample images x₀ from dataset
///     2. Sample timesteps t uniformly
///     3. Sample noise ε ~ N(0, I)
///     4. Create noisy images x_t
///     5. Predict noise ε_θ(x_t, t)
///     6. Compute loss ||ε - ε_θ||²
///     7. Update model parameters
///     8. Update EMA parameters
/// ```
///
/// <b>Evaluation</b>:
/// - Generate samples every 10K steps
/// - Compute FID (Frechet Inception Distance)
/// - Visual inspection of sample quality
/// </remarks>
public class DDPMTrainer<T>
{
    // TODO: Implement full training loop with:
    // - Data loading and batching
    // - Adam optimizer
    // - EMA for stable generation
    // - Gradient clipping
    // - Checkpointing
    // - FID evaluation
    // - Tensorboard logging
}

Expected Results

Dataset	Image Size	FID Score	Training Time
CIFAR-10	32×32	3.17	~5 days on 8 V100 GPUs
CelebA-HQ	256×256	5.11	~14 days on 8 V100 GPUs
ImageNet	256×256	7.72	~21 days on 8 V100 GPUs

Common Pitfalls

Pitfall 1: Incorrect Noise Scaling

Problem: Images don't denoise properly or become artifacts. Solution: Verify alpha_bar computation and noise scaling factors.

Pitfall 2: Timestep Embedding Issues

Problem: Model can't distinguish between timesteps. Solution: Ensure sinusoidal embeddings cover full frequency range.

Pitfall 3: Numerical Instability

Problem: NaN or Inf values during training. Solution: Use gradient clipping, check scheduler values, verify softmax stability.

Pitfall 4: Too Few Sampling Steps

Problem: Generated images are blurry or noisy. Solution: Use at least 250 steps for DDPM, or implement DDIM for faster sampling.

Pitfall 5: Poor U-Net Architecture

Problem: Model can't capture fine details. Solution: Use attention blocks at lower resolutions, increase model capacity.

Performance Benchmarks

Computational Requirements

Component	Parameters	Memory	Training Time (1M images)
U-Net (Small)	35M	~4 GB	~3 days (8 GPUs)
U-Net (Base)	100M	~12 GB	~7 days (8 GPUs)
U-Net (Large)	400M	~40 GB	~14 days (8 GPUs)

Generation Speed

Method	Steps	Time per Image (256×256)
DDPM	1000	~10 seconds
DDIM	50	~0.5 seconds
DDIM	250	~2.5 seconds

Next Steps

Implement DDIM Sampling: Much faster inference
Add Conditioning:
- Class-conditional generation
- Text-to-image (CLIP guidance)
Latent Diffusion:
- VAE encoder/decoder
- Work in compressed latent space
Advanced Features:
- Classifier-free guidance
- Inpainting and editing
- Super-resolution

Resources

Nov 07 '25 04:11 ooples

[Phase 3] Implement Self-Supervised Learning Methods

Problem

Missing Implementations

Architecture

Success Criteria

Junior Developer Implementation Guide: Issue #395

Diffusion Models (DDPM, Stable Diffusion)

Overview

Understanding Diffusion Models

What Are Diffusion Models?

Why Diffusion Models Are Powerful

Key Concepts

1. Forward Diffusion Process (Adding Noise)

2. Noise Schedules

3. Reverse Diffusion (Denoising)

4. DDPM (Denoising Diffusion Probabilistic Models)

5. DDIM (Denoising Diffusion Implicit Models)

6. Stable Diffusion

Architecture Overview

File Structure

Class Hierarchy

Step-by-Step Implementation

Step 1: Core Interfaces

File: src/Interfaces/INoiseScheduler.cs

File: src/Interfaces/IDiffusionModel.cs

Step 2: Noise Schedulers

File: src/Diffusion/Schedulers/NoiseScheduler.cs

File: src/Diffusion/Schedulers/LinearSchedule.cs

Step 3: Time Embeddings

File: src/Diffusion/UNet/TimeEmbedding.cs

Step 4: U-Net Architecture (Simplified)

File: src/Interfaces/IUNet.cs

Step 5: DDPM Model

File: src/Models/Generative/Diffusion/DDPMModel.cs

Testing Strategy

Unit Tests

Training Strategy

DDPM Training

Expected Results

Common Pitfalls

Pitfall 1: Incorrect Noise Scaling

Pitfall 2: Timestep Embedding Issues

Pitfall 3: Numerical Instability

Pitfall 4: Too Few Sampling Steps

Pitfall 5: Poor U-Net Architecture

Performance Benchmarks

Computational Requirements

Generation Speed

Next Steps

Resources

File: `src/Interfaces/INoiseScheduler.cs`

File: `src/Interfaces/IDiffusionModel.cs`

File: `src/Diffusion/Schedulers/NoiseScheduler.cs`

File: `src/Diffusion/Schedulers/LinearSchedule.cs`

File: `src/Diffusion/UNet/TimeEmbedding.cs`

File: `src/Interfaces/IUNet.cs`

File: `src/Models/Generative/Diffusion/DDPMModel.cs`