### How to Build a diffusion Model From Scratch

Diffusion models are a type of generative deep learning model that can generate new samples that are similar to the original dataset. In this blog post, we will discuss how to build a diffusion model from scratch using Python and TensorFlow. We will also explore the mathematics and intuition behind diffusion models.

# Understanding Diffusion Models

Diffusion models are generative models that work by destroying training data through the successive addition of Gaussian noise and then learning to recover the data by reversing this noising process. The diffusion process is the core of the diffusion model. It involves a sequence of noise-reducing transformations that are applied to the input data. The diffusion process is defined as follows:
• Start with a sequence of Gaussian noise with a mean of 0 and unit variance.
• Apply a sequence of noise-reducing transformations to the noise sequence.
• The output of the diffusion process is the final noise sequence.
• The diffusion process is what makes the diffusion model unique. It allows the model to generate new samples that are similar to the original dataset.

# Defining the CNN Architecture

The CNN architecture for the diffusion model is defined as follows:
import tensorflow as tf
from tensorflow.keras import layers

def make_diffusion_model():
model = tf.keras.Sequential()
for i in range(10):
return model
The CNN architecture consists of 10 convolutional layers with 64 filters and a kernel size of 3x3. Each convolutional layer is followed by a batch normalization layer and a ReLU activation function. The final convolutional layer has 3 filters and a kernel size of 1x1.

# Implementing the Diffusion Process

To implement the diffusion process, we can use the following code:
import tensorflow as tf

def diffusion_process(x, timesteps=1000):

for i in range(timesteps):

noise = tf.random.normal(shape=x.shape)

x = x + tf.math.sqrt(2.0 * 0.01) * noise

x = x / tf.math.sqrt(1.0 + 2.0 * 0.01)

x = make_diffusion_model()(x)

return x
The diffusion_process function takes a sequence of Gaussian noise and applies the diffusion process to it. The function applies the diffusion process for a specified number of timesteps, which is set to 1000 by default. The function uses the make_diffusion_model function to define the CNN architecture for the diffusion model.

## Training the Model

To train the model, we will use the CIFAR-10 dataset provided by TensorFlow. We will train the model using stochastic gradient descent (SGD) with a learning rate of 0.001 and a batch size of 64. We will train the model for 100 epochs.
import tensorflow_datasets as tfds

def train_diffusion_model():

dataset = dataset.batch(64).prefetch(tf.data.AUTOTUNE)

optimizer = tf.keras.optimizers.SGD(learning_rate=0.001)

for epoch in range(100):

for batch in dataset:

noise = tf.random.normal(shape=batch.shape)

diffused_noise = diffusion_process(noise)

logits = make_diffusion_model()(diffused_noise, training=True)

loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(batch, logits))

print(f'Epoch {epoch + 1}, Loss: {loss.numpy()}')

# Save the weights of the trained model

model.save_weights('diffusion_model.h5')

# Load the saved weights into a new model object

new_model = make_diffusion_model()

new_model.load_weights('diffusion_model.h5')
The train_diffusion_model function loads the CIFAR-10 dataset and trains the diffusion model using stochastic gradient descent. We use the diffusion_process function to apply the diffusion process to a sequence of Gaussian noise.

# Generating New Samples

Once the model is trained, we can generate new samples by applying the diffusion process to a sequence of Gaussian noise. We can then use the trained model to generate new samples from the final noise sequence.
import matplotlib.pyplot as plt

def generate_samples():

noise = tf.random.normal(shape=(1, 32, 32, 3))

diffused_noise = diffusion_process(noise)

model = make_diffusion_model()

for i in range(10):

logits = model(diffused_noise, training=False)

probs = tf.nn.softmax(logits)

sample = tf.random.categorical(probs, num_samples=1)

sample = tf.squeeze(sample, axis=-1)

sample = tf.cast(sample, tf.float32) / 255.0

diffused_noise = diffusion_process(sample)

plt.imshow(sample.numpy())

plt.show()
The generate_samples function generates 10 new samples using the trained diffusion model. We start with a sequence of Gaussian noise and apply the diffusion process to generate the final noise sequence. We then use the trained model to generate new samples from the final noise sequence.

# Conclusion

In this blog post, we discussed how to build a diffusion model from scratch using Python and TensorFlow. We defined the diffusion process and the CNN architecture for the diffusion model. We trained the model using the CIFAR-10 dataset and generated new samples using the trained model. We also explored the mathematics and intuition behind diffusion models. The diffusion model is a powerful generative deep learning model that can be used to generate new samples that are similar to the original dataset.