# Chapter 10: Project: Image Generation with Diffusion Models

## 10.5 Evaluating the Model

Evaluating the performance of the diffusion model is essential to ensure that the generated images are of high quality, coherent, and contextually appropriate. This section will cover various methods to evaluate the model, including quantitative metrics and qualitative assessments. We will provide detailed explanations and example codes for each evaluation method.

### 10.5.1 Quantitative Evaluation Metrics

Quantitative metrics provide objective measures of the model's performance. Common metrics for evaluating image generation models include Mean Squared Error (MSE), Fréchet Inception Distance (FID), and Inception Score (IS). These metrics help assess the quality, diversity, and realism of the generated images.

**Mean Squared Error (MSE)**

MSE measures the average squared difference between the original and generated images. Lower MSE values indicate better performance, as they imply that the generated images closely resemble the original images.

**Example: Calculating MSE**

`import numpy as np`

from sklearn.metrics import mean_squared_error

# Generate synthetic test data

test_data = generate_synthetic_data(100, noise_shape[0], noise_shape[1], noise_shape[2])

noisy_test_data = [noise_layer(data, training=True) for data in test_data]

X_test = np.array([noisy[-1] for noisy in noisy_test_data])

y_test = np.array([data for data in test_data])

# Predict denoised data

denoised_data = diffusion_model.predict(X_test)

# Calculate MSE

mse = mean_squared_error(y_test.flatten(), denoised_data.flatten())

print(f"MSE: {mse}")

This script is using the NumPy and sklearn library to create synthetic test data, add noise to this data, and then attempt to denoise it using a model called 'diffusion_model'. Afterwards, it calculates the Mean Squared Error (MSE) between the original and the denoised data, which is a common metric to evaluate the performance of a regression model. The lower the MSE, the better the model's performance.

**Fréchet Inception Distance (FID)**

FID measures the distance between the distributions of the original and generated images, capturing both the quality and diversity of the generated images. Lower FID scores indicate better performance.

**Example: Calculating FID**

`from scipy.linalg import sqrtm`

from numpy import cov, trace, iscomplexobj

def calculate_fid(real_images, generated_images):

# Calculate the mean and covariance of real and generated images

mu1, sigma1 = real_images.mean(axis=0), cov(real_images, rowvar=False)

mu2, sigma2 = generated_images.mean(axis=0), cov(generated_images, rowvar=False)

# Calculate the sum of squared differences between means

ssdiff = np.sum((mu1 - mu2) ** 2.0)

# Calculate the square root of the product of covariances

covmean = sqrtm(sigma1.dot(sigma2))

if iscomplexobj(covmean):

covmean = covmean.real

# Calculate the FID score

fid = ssdiff + trace(sigma1 + sigma2 - 2.0 * covmean)

return fid

# Assume denoised_data and y_test are the denoised and original data, respectively

fid_score = calculate_fid(y_test.reshape(100, -1), denoised_data.reshape(100, -1))

print(f"FID Score: {fid_score}")

The code defines a function, `calculate_fid`

, for calculating the Frechet Inception Distance (FID) between real and generated images. The FID is a measure of similarity between two sets of images, commonly used to evaluate the quality of images generated by Generative Adversarial Networks (GANs).

The function calculates the mean and covariance of both real and generated images. It then computes the sum of squared differences between the means and the square root of the product of covariances. If the result is complex, it only takes the real part. The FID score is then calculated as the sum of the squared difference of the means and the trace of the sum of the covariances minus twice the product of the covariances.

The last part of the code uses the defined function to calculate the FID score between `y_test`

and `denoised_data`

(presumably the original and denoised data), reshaping them before passing them to the function. The FID score is then printed.

**Inception Score (IS)**

IS evaluates the quality and diversity of generated images based on the predictions of a pre-trained Inception network. Higher IS values indicate better performance.

**Example: Calculating Inception Score**

`import tensorflow as tf`

from tensorflow.keras.applications.inception_v3 import InceptionV3, preprocess_input

from scipy.stats import entropy

# Load the pre-trained InceptionV3 model

inception_model = InceptionV3(include_top=False, pooling='avg', input_shape=(299, 299, 3))

def calculate_inception_score(images, n_split=10, eps=1E-16):

# Resize and preprocess images for InceptionV3 model

images_resized = tf.image.resize(images, (299, 299))

images_preprocessed = preprocess_input(images_resized)

# Predict using the InceptionV3 model

preds = inception_model.predict(images_preprocessed)

# Calculate Inception Score

split_scores = []

for i in range(n_split):

part = preds[i * preds.shape[0] // n_split: (i + 1) * preds.shape[0] // n_split]

py = np.mean(part, axis=0)

scores = []

for p in part:

scores.append(entropy(p, py))

split_scores.append(np.exp(np.mean(scores)))

return np.mean(split_scores), np.std(split_scores)

# Assume denoised_data are the generated images

is_mean, is_std = calculate_inception_score(denoised_data)

print(f"Inception Score: {is_mean} ± {is_std}")

This code uses the TensorFlow library and its InceptionV3 model, a pre-trained neural network for image classification, to calculate the Inception Score of a set of images.

The Inception Score is a measure used to evaluate the quality of images generated by Generative Adversarial Networks (GANs). It assesses both the variety of images produced (using entropy) and how realistic they are (how well they are classified by the Inception model).

The script first loads the InceptionV3 model. Next, it defines a function to calculate the Inception Score. Images are resized and preprocessed to match the input requirements of the InceptionV3 model. The model is then used to make predictions on the preprocessed images. These predictions are used to calculate the Inception Score. The function returns the mean and standard deviation of the scores.

Finally, it assumes that `denoised_data`

are the generated images, and it calculates their Inception Score, printing the mean and standard deviation.

### 10.5.2 Qualitative Evaluation

Qualitative evaluation involves visually inspecting the generated images to assess their quality, coherence, and realism. This method is subjective but provides valuable insights into the model's performance.

**Visual Inspection**

Visual inspection involves generating a set of images and examining them for quality and coherence. This helps identify any obvious issues such as artifacts, blurriness, or unrealistic features.

**Example: Visual Inspection**

`import matplotlib.pyplot as plt`

# Generate a sample for visual inspection

plt.figure(figsize=(12, 4))

for i in range(batch_size):

plt.subplot(2, 5, i + 1)

plt.imshow((generated_images[i] * 0.5) + 0.5)

plt.axis('off')

plt.suptitle('Generated Images')

plt.show()

This script uses the matplotlib library to generate and display the set of images. After importing the library, it opens a new figure with a specified size. It then generates a number of images equal to 'batch_size' (which is not defined in the selected text).

For each image, it creates a subplot, generates the image (apparently from some form of image data, also not defined in the selected text), adjusts the image's color range and removes the axis. Once all images have been generated, it adds a title ('Generated Images') to the figure and displays it.

**Human Evaluation**

Human evaluation involves asking a group of people to rate the quality of the generated images based on criteria such as realism, coherence, and overall quality. This method provides a robust assessment of the model's performance but can be time-consuming and resource-intensive.

**Example: Human Evaluation Criteria**

**Realism**: Does the generated image look realistic?**Coherence**: Is the generated image consistent and free of artifacts?**Overall Quality**: How does the generated image compare to real images?

### 10.5.3 Evaluating Diversity and Creativity

To assess the diversity and creativity of the generated images, we can analyze the variation in outputs given different inputs or slight variations of the same input. This helps ensure that the model produces diverse and interesting outputs.

**Example: Evaluating Diversity**

`# Define a set of inputs with slight variations`

inputs = [

random_noise[0],

random_noise[1],

random_noise[2],

]

# Generate and plot outputs for each input

plt.figure(figsize=(12, 4))

for i, input_data in enumerate(inputs):

step_encodings = create_step_encodings(1, d_model)

output = diffusion_model.predict([np.expand_dims(input_data, axis=0), step_encodings])[0]

plt.subplot(1, 3, i + 1)

plt.imshow((output * 0.5) + 0.5)

plt.axis('off')

plt.title(f'Generated Image {i+1}')

plt.show()

This script generates and plots the images using a predictive model. It starts by defining a set of inputs that are variants of 'random_noise'. Then, for each input, it creates step encodings, predicts the output using the 'diffusion_model', and plots the generated image. The images are plotted in a 1 row by 3 columns grid and labeled as 'Generated Image 1', 'Generated Image 2', and 'Generated Image 3'. The final line of code displays the plotted images.

**Summary**

In this section, we discussed various methods for evaluating the performance of the diffusion model, including both quantitative metrics and qualitative assessments. Quantitative metrics such as Mean Squared Error (MSE), Fréchet Inception Distance (FID), and Inception Score (IS) provide objective measures of the model's performance, assessing the quality, diversity, and realism of the generated images.

We also explored qualitative evaluation methods, including visual inspection and human evaluation, which offer valuable insights into the model's performance from a subjective perspective. Evaluating the diversity and creativity of the generated images ensures that the model produces varied and interesting outputs.

By combining these evaluation techniques, you can gain a comprehensive understanding of the model's strengths and areas for improvement, ultimately enhancing its ability to generate high-quality images.

## 10.5 Evaluating the Model

Evaluating the performance of the diffusion model is essential to ensure that the generated images are of high quality, coherent, and contextually appropriate. This section will cover various methods to evaluate the model, including quantitative metrics and qualitative assessments. We will provide detailed explanations and example codes for each evaluation method.

### 10.5.1 Quantitative Evaluation Metrics

Quantitative metrics provide objective measures of the model's performance. Common metrics for evaluating image generation models include Mean Squared Error (MSE), Fréchet Inception Distance (FID), and Inception Score (IS). These metrics help assess the quality, diversity, and realism of the generated images.

**Mean Squared Error (MSE)**

MSE measures the average squared difference between the original and generated images. Lower MSE values indicate better performance, as they imply that the generated images closely resemble the original images.

**Example: Calculating MSE**

`import numpy as np`

from sklearn.metrics import mean_squared_error

# Generate synthetic test data

test_data = generate_synthetic_data(100, noise_shape[0], noise_shape[1], noise_shape[2])

noisy_test_data = [noise_layer(data, training=True) for data in test_data]

X_test = np.array([noisy[-1] for noisy in noisy_test_data])

y_test = np.array([data for data in test_data])

# Predict denoised data

denoised_data = diffusion_model.predict(X_test)

# Calculate MSE

mse = mean_squared_error(y_test.flatten(), denoised_data.flatten())

print(f"MSE: {mse}")

This script is using the NumPy and sklearn library to create synthetic test data, add noise to this data, and then attempt to denoise it using a model called 'diffusion_model'. Afterwards, it calculates the Mean Squared Error (MSE) between the original and the denoised data, which is a common metric to evaluate the performance of a regression model. The lower the MSE, the better the model's performance.

**Fréchet Inception Distance (FID)**

FID measures the distance between the distributions of the original and generated images, capturing both the quality and diversity of the generated images. Lower FID scores indicate better performance.

**Example: Calculating FID**

`from scipy.linalg import sqrtm`

from numpy import cov, trace, iscomplexobj

def calculate_fid(real_images, generated_images):

# Calculate the mean and covariance of real and generated images

mu1, sigma1 = real_images.mean(axis=0), cov(real_images, rowvar=False)

mu2, sigma2 = generated_images.mean(axis=0), cov(generated_images, rowvar=False)

# Calculate the sum of squared differences between means

ssdiff = np.sum((mu1 - mu2) ** 2.0)

# Calculate the square root of the product of covariances

covmean = sqrtm(sigma1.dot(sigma2))

if iscomplexobj(covmean):

covmean = covmean.real

# Calculate the FID score

fid = ssdiff + trace(sigma1 + sigma2 - 2.0 * covmean)

return fid

# Assume denoised_data and y_test are the denoised and original data, respectively

fid_score = calculate_fid(y_test.reshape(100, -1), denoised_data.reshape(100, -1))

print(f"FID Score: {fid_score}")

The code defines a function, `calculate_fid`

, for calculating the Frechet Inception Distance (FID) between real and generated images. The FID is a measure of similarity between two sets of images, commonly used to evaluate the quality of images generated by Generative Adversarial Networks (GANs).

The function calculates the mean and covariance of both real and generated images. It then computes the sum of squared differences between the means and the square root of the product of covariances. If the result is complex, it only takes the real part. The FID score is then calculated as the sum of the squared difference of the means and the trace of the sum of the covariances minus twice the product of the covariances.

The last part of the code uses the defined function to calculate the FID score between `y_test`

and `denoised_data`

(presumably the original and denoised data), reshaping them before passing them to the function. The FID score is then printed.

**Inception Score (IS)**

IS evaluates the quality and diversity of generated images based on the predictions of a pre-trained Inception network. Higher IS values indicate better performance.

**Example: Calculating Inception Score**

`import tensorflow as tf`

from tensorflow.keras.applications.inception_v3 import InceptionV3, preprocess_input

from scipy.stats import entropy

# Load the pre-trained InceptionV3 model

inception_model = InceptionV3(include_top=False, pooling='avg', input_shape=(299, 299, 3))

def calculate_inception_score(images, n_split=10, eps=1E-16):

# Resize and preprocess images for InceptionV3 model

images_resized = tf.image.resize(images, (299, 299))

images_preprocessed = preprocess_input(images_resized)

# Predict using the InceptionV3 model

preds = inception_model.predict(images_preprocessed)

# Calculate Inception Score

split_scores = []

for i in range(n_split):

part = preds[i * preds.shape[0] // n_split: (i + 1) * preds.shape[0] // n_split]

py = np.mean(part, axis=0)

scores = []

for p in part:

scores.append(entropy(p, py))

split_scores.append(np.exp(np.mean(scores)))

return np.mean(split_scores), np.std(split_scores)

# Assume denoised_data are the generated images

is_mean, is_std = calculate_inception_score(denoised_data)

print(f"Inception Score: {is_mean} ± {is_std}")

This code uses the TensorFlow library and its InceptionV3 model, a pre-trained neural network for image classification, to calculate the Inception Score of a set of images.

The Inception Score is a measure used to evaluate the quality of images generated by Generative Adversarial Networks (GANs). It assesses both the variety of images produced (using entropy) and how realistic they are (how well they are classified by the Inception model).

The script first loads the InceptionV3 model. Next, it defines a function to calculate the Inception Score. Images are resized and preprocessed to match the input requirements of the InceptionV3 model. The model is then used to make predictions on the preprocessed images. These predictions are used to calculate the Inception Score. The function returns the mean and standard deviation of the scores.

Finally, it assumes that `denoised_data`

are the generated images, and it calculates their Inception Score, printing the mean and standard deviation.

### 10.5.2 Qualitative Evaluation

Qualitative evaluation involves visually inspecting the generated images to assess their quality, coherence, and realism. This method is subjective but provides valuable insights into the model's performance.

**Visual Inspection**

Visual inspection involves generating a set of images and examining them for quality and coherence. This helps identify any obvious issues such as artifacts, blurriness, or unrealistic features.

**Example: Visual Inspection**

`import matplotlib.pyplot as plt`

# Generate a sample for visual inspection

plt.figure(figsize=(12, 4))

for i in range(batch_size):

plt.subplot(2, 5, i + 1)

plt.imshow((generated_images[i] * 0.5) + 0.5)

plt.axis('off')

plt.suptitle('Generated Images')

plt.show()

This script uses the matplotlib library to generate and display the set of images. After importing the library, it opens a new figure with a specified size. It then generates a number of images equal to 'batch_size' (which is not defined in the selected text).

For each image, it creates a subplot, generates the image (apparently from some form of image data, also not defined in the selected text), adjusts the image's color range and removes the axis. Once all images have been generated, it adds a title ('Generated Images') to the figure and displays it.

**Human Evaluation**

Human evaluation involves asking a group of people to rate the quality of the generated images based on criteria such as realism, coherence, and overall quality. This method provides a robust assessment of the model's performance but can be time-consuming and resource-intensive.

**Example: Human Evaluation Criteria**

**Realism**: Does the generated image look realistic?**Coherence**: Is the generated image consistent and free of artifacts?**Overall Quality**: How does the generated image compare to real images?

### 10.5.3 Evaluating Diversity and Creativity

To assess the diversity and creativity of the generated images, we can analyze the variation in outputs given different inputs or slight variations of the same input. This helps ensure that the model produces diverse and interesting outputs.

**Example: Evaluating Diversity**

`# Define a set of inputs with slight variations`

inputs = [

random_noise[0],

random_noise[1],

random_noise[2],

]

# Generate and plot outputs for each input

plt.figure(figsize=(12, 4))

for i, input_data in enumerate(inputs):

step_encodings = create_step_encodings(1, d_model)

output = diffusion_model.predict([np.expand_dims(input_data, axis=0), step_encodings])[0]

plt.subplot(1, 3, i + 1)

plt.imshow((output * 0.5) + 0.5)

plt.axis('off')

plt.title(f'Generated Image {i+1}')

plt.show()

This script generates and plots the images using a predictive model. It starts by defining a set of inputs that are variants of 'random_noise'. Then, for each input, it creates step encodings, predicts the output using the 'diffusion_model', and plots the generated image. The images are plotted in a 1 row by 3 columns grid and labeled as 'Generated Image 1', 'Generated Image 2', and 'Generated Image 3'. The final line of code displays the plotted images.

**Summary**

In this section, we discussed various methods for evaluating the performance of the diffusion model, including both quantitative metrics and qualitative assessments. Quantitative metrics such as Mean Squared Error (MSE), Fréchet Inception Distance (FID), and Inception Score (IS) provide objective measures of the model's performance, assessing the quality, diversity, and realism of the generated images.

We also explored qualitative evaluation methods, including visual inspection and human evaluation, which offer valuable insights into the model's performance from a subjective perspective. Evaluating the diversity and creativity of the generated images ensures that the model produces varied and interesting outputs.

By combining these evaluation techniques, you can gain a comprehensive understanding of the model's strengths and areas for improvement, ultimately enhancing its ability to generate high-quality images.

## 10.5 Evaluating the Model

Evaluating the performance of the diffusion model is essential to ensure that the generated images are of high quality, coherent, and contextually appropriate. This section will cover various methods to evaluate the model, including quantitative metrics and qualitative assessments. We will provide detailed explanations and example codes for each evaluation method.

### 10.5.1 Quantitative Evaluation Metrics

Quantitative metrics provide objective measures of the model's performance. Common metrics for evaluating image generation models include Mean Squared Error (MSE), Fréchet Inception Distance (FID), and Inception Score (IS). These metrics help assess the quality, diversity, and realism of the generated images.

**Mean Squared Error (MSE)**

MSE measures the average squared difference between the original and generated images. Lower MSE values indicate better performance, as they imply that the generated images closely resemble the original images.

**Example: Calculating MSE**

`import numpy as np`

from sklearn.metrics import mean_squared_error

# Generate synthetic test data

test_data = generate_synthetic_data(100, noise_shape[0], noise_shape[1], noise_shape[2])

noisy_test_data = [noise_layer(data, training=True) for data in test_data]

X_test = np.array([noisy[-1] for noisy in noisy_test_data])

y_test = np.array([data for data in test_data])

# Predict denoised data

denoised_data = diffusion_model.predict(X_test)

# Calculate MSE

mse = mean_squared_error(y_test.flatten(), denoised_data.flatten())

print(f"MSE: {mse}")

This script is using the NumPy and sklearn library to create synthetic test data, add noise to this data, and then attempt to denoise it using a model called 'diffusion_model'. Afterwards, it calculates the Mean Squared Error (MSE) between the original and the denoised data, which is a common metric to evaluate the performance of a regression model. The lower the MSE, the better the model's performance.

**Fréchet Inception Distance (FID)**

FID measures the distance between the distributions of the original and generated images, capturing both the quality and diversity of the generated images. Lower FID scores indicate better performance.

**Example: Calculating FID**

`from scipy.linalg import sqrtm`

from numpy import cov, trace, iscomplexobj

def calculate_fid(real_images, generated_images):

# Calculate the mean and covariance of real and generated images

mu1, sigma1 = real_images.mean(axis=0), cov(real_images, rowvar=False)

mu2, sigma2 = generated_images.mean(axis=0), cov(generated_images, rowvar=False)

# Calculate the sum of squared differences between means

ssdiff = np.sum((mu1 - mu2) ** 2.0)

# Calculate the square root of the product of covariances

covmean = sqrtm(sigma1.dot(sigma2))

if iscomplexobj(covmean):

covmean = covmean.real

# Calculate the FID score

fid = ssdiff + trace(sigma1 + sigma2 - 2.0 * covmean)

return fid

# Assume denoised_data and y_test are the denoised and original data, respectively

fid_score = calculate_fid(y_test.reshape(100, -1), denoised_data.reshape(100, -1))

print(f"FID Score: {fid_score}")

The code defines a function, `calculate_fid`

, for calculating the Frechet Inception Distance (FID) between real and generated images. The FID is a measure of similarity between two sets of images, commonly used to evaluate the quality of images generated by Generative Adversarial Networks (GANs).

The function calculates the mean and covariance of both real and generated images. It then computes the sum of squared differences between the means and the square root of the product of covariances. If the result is complex, it only takes the real part. The FID score is then calculated as the sum of the squared difference of the means and the trace of the sum of the covariances minus twice the product of the covariances.

The last part of the code uses the defined function to calculate the FID score between `y_test`

and `denoised_data`

(presumably the original and denoised data), reshaping them before passing them to the function. The FID score is then printed.

**Inception Score (IS)**

IS evaluates the quality and diversity of generated images based on the predictions of a pre-trained Inception network. Higher IS values indicate better performance.

**Example: Calculating Inception Score**

`import tensorflow as tf`

from tensorflow.keras.applications.inception_v3 import InceptionV3, preprocess_input

from scipy.stats import entropy

# Load the pre-trained InceptionV3 model

inception_model = InceptionV3(include_top=False, pooling='avg', input_shape=(299, 299, 3))

def calculate_inception_score(images, n_split=10, eps=1E-16):

# Resize and preprocess images for InceptionV3 model

images_resized = tf.image.resize(images, (299, 299))

images_preprocessed = preprocess_input(images_resized)

# Predict using the InceptionV3 model

preds = inception_model.predict(images_preprocessed)

# Calculate Inception Score

split_scores = []

for i in range(n_split):

part = preds[i * preds.shape[0] // n_split: (i + 1) * preds.shape[0] // n_split]

py = np.mean(part, axis=0)

scores = []

for p in part:

scores.append(entropy(p, py))

split_scores.append(np.exp(np.mean(scores)))

return np.mean(split_scores), np.std(split_scores)

# Assume denoised_data are the generated images

is_mean, is_std = calculate_inception_score(denoised_data)

print(f"Inception Score: {is_mean} ± {is_std}")

This code uses the TensorFlow library and its InceptionV3 model, a pre-trained neural network for image classification, to calculate the Inception Score of a set of images.

The Inception Score is a measure used to evaluate the quality of images generated by Generative Adversarial Networks (GANs). It assesses both the variety of images produced (using entropy) and how realistic they are (how well they are classified by the Inception model).

The script first loads the InceptionV3 model. Next, it defines a function to calculate the Inception Score. Images are resized and preprocessed to match the input requirements of the InceptionV3 model. The model is then used to make predictions on the preprocessed images. These predictions are used to calculate the Inception Score. The function returns the mean and standard deviation of the scores.

Finally, it assumes that `denoised_data`

are the generated images, and it calculates their Inception Score, printing the mean and standard deviation.

### 10.5.2 Qualitative Evaluation

Qualitative evaluation involves visually inspecting the generated images to assess their quality, coherence, and realism. This method is subjective but provides valuable insights into the model's performance.

**Visual Inspection**

Visual inspection involves generating a set of images and examining them for quality and coherence. This helps identify any obvious issues such as artifacts, blurriness, or unrealistic features.

**Example: Visual Inspection**

`import matplotlib.pyplot as plt`

# Generate a sample for visual inspection

plt.figure(figsize=(12, 4))

for i in range(batch_size):

plt.subplot(2, 5, i + 1)

plt.imshow((generated_images[i] * 0.5) + 0.5)

plt.axis('off')

plt.suptitle('Generated Images')

plt.show()

This script uses the matplotlib library to generate and display the set of images. After importing the library, it opens a new figure with a specified size. It then generates a number of images equal to 'batch_size' (which is not defined in the selected text).

For each image, it creates a subplot, generates the image (apparently from some form of image data, also not defined in the selected text), adjusts the image's color range and removes the axis. Once all images have been generated, it adds a title ('Generated Images') to the figure and displays it.

**Human Evaluation**

Human evaluation involves asking a group of people to rate the quality of the generated images based on criteria such as realism, coherence, and overall quality. This method provides a robust assessment of the model's performance but can be time-consuming and resource-intensive.

**Example: Human Evaluation Criteria**

**Realism**: Does the generated image look realistic?**Coherence**: Is the generated image consistent and free of artifacts?**Overall Quality**: How does the generated image compare to real images?

### 10.5.3 Evaluating Diversity and Creativity

To assess the diversity and creativity of the generated images, we can analyze the variation in outputs given different inputs or slight variations of the same input. This helps ensure that the model produces diverse and interesting outputs.

**Example: Evaluating Diversity**

`# Define a set of inputs with slight variations`

inputs = [

random_noise[0],

random_noise[1],

random_noise[2],

]

# Generate and plot outputs for each input

plt.figure(figsize=(12, 4))

for i, input_data in enumerate(inputs):

step_encodings = create_step_encodings(1, d_model)

output = diffusion_model.predict([np.expand_dims(input_data, axis=0), step_encodings])[0]

plt.subplot(1, 3, i + 1)

plt.imshow((output * 0.5) + 0.5)

plt.axis('off')

plt.title(f'Generated Image {i+1}')

plt.show()

This script generates and plots the images using a predictive model. It starts by defining a set of inputs that are variants of 'random_noise'. Then, for each input, it creates step encodings, predicts the output using the 'diffusion_model', and plots the generated image. The images are plotted in a 1 row by 3 columns grid and labeled as 'Generated Image 1', 'Generated Image 2', and 'Generated Image 3'. The final line of code displays the plotted images.

**Summary**

In this section, we discussed various methods for evaluating the performance of the diffusion model, including both quantitative metrics and qualitative assessments. Quantitative metrics such as Mean Squared Error (MSE), Fréchet Inception Distance (FID), and Inception Score (IS) provide objective measures of the model's performance, assessing the quality, diversity, and realism of the generated images.

We also explored qualitative evaluation methods, including visual inspection and human evaluation, which offer valuable insights into the model's performance from a subjective perspective. Evaluating the diversity and creativity of the generated images ensures that the model produces varied and interesting outputs.

By combining these evaluation techniques, you can gain a comprehensive understanding of the model's strengths and areas for improvement, ultimately enhancing its ability to generate high-quality images.

## 10.5 Evaluating the Model

### 10.5.1 Quantitative Evaluation Metrics

**Mean Squared Error (MSE)**

**Example: Calculating MSE**

`import numpy as np`

from sklearn.metrics import mean_squared_error

# Generate synthetic test data

test_data = generate_synthetic_data(100, noise_shape[0], noise_shape[1], noise_shape[2])

noisy_test_data = [noise_layer(data, training=True) for data in test_data]

X_test = np.array([noisy[-1] for noisy in noisy_test_data])

y_test = np.array([data for data in test_data])

# Predict denoised data

denoised_data = diffusion_model.predict(X_test)

# Calculate MSE

mse = mean_squared_error(y_test.flatten(), denoised_data.flatten())

print(f"MSE: {mse}")

**Fréchet Inception Distance (FID)**

**Example: Calculating FID**

`from scipy.linalg import sqrtm`

from numpy import cov, trace, iscomplexobj

def calculate_fid(real_images, generated_images):

# Calculate the mean and covariance of real and generated images

mu1, sigma1 = real_images.mean(axis=0), cov(real_images, rowvar=False)

mu2, sigma2 = generated_images.mean(axis=0), cov(generated_images, rowvar=False)

# Calculate the sum of squared differences between means

ssdiff = np.sum((mu1 - mu2) ** 2.0)

# Calculate the square root of the product of covariances

covmean = sqrtm(sigma1.dot(sigma2))

if iscomplexobj(covmean):

covmean = covmean.real

# Calculate the FID score

fid = ssdiff + trace(sigma1 + sigma2 - 2.0 * covmean)

return fid

# Assume denoised_data and y_test are the denoised and original data, respectively

fid_score = calculate_fid(y_test.reshape(100, -1), denoised_data.reshape(100, -1))

print(f"FID Score: {fid_score}")

`calculate_fid`

, for calculating the Frechet Inception Distance (FID) between real and generated images. The FID is a measure of similarity between two sets of images, commonly used to evaluate the quality of images generated by Generative Adversarial Networks (GANs).

`y_test`

and `denoised_data`

(presumably the original and denoised data), reshaping them before passing them to the function. The FID score is then printed.

**Inception Score (IS)**

**Example: Calculating Inception Score**

`import tensorflow as tf`

from tensorflow.keras.applications.inception_v3 import InceptionV3, preprocess_input

from scipy.stats import entropy

# Load the pre-trained InceptionV3 model

inception_model = InceptionV3(include_top=False, pooling='avg', input_shape=(299, 299, 3))

def calculate_inception_score(images, n_split=10, eps=1E-16):

# Resize and preprocess images for InceptionV3 model

images_resized = tf.image.resize(images, (299, 299))

images_preprocessed = preprocess_input(images_resized)

# Predict using the InceptionV3 model

preds = inception_model.predict(images_preprocessed)

# Calculate Inception Score

split_scores = []

for i in range(n_split):

part = preds[i * preds.shape[0] // n_split: (i + 1) * preds.shape[0] // n_split]

py = np.mean(part, axis=0)

scores = []

for p in part:

scores.append(entropy(p, py))

split_scores.append(np.exp(np.mean(scores)))

return np.mean(split_scores), np.std(split_scores)

# Assume denoised_data are the generated images

is_mean, is_std = calculate_inception_score(denoised_data)

print(f"Inception Score: {is_mean} ± {is_std}")

`denoised_data`

are the generated images, and it calculates their Inception Score, printing the mean and standard deviation.

### 10.5.2 Qualitative Evaluation

**Visual Inspection**

**Example: Visual Inspection**

`import matplotlib.pyplot as plt`

# Generate a sample for visual inspection

plt.figure(figsize=(12, 4))

for i in range(batch_size):

plt.subplot(2, 5, i + 1)

plt.imshow((generated_images[i] * 0.5) + 0.5)

plt.axis('off')

plt.suptitle('Generated Images')

plt.show()

**Human Evaluation**

**Example: Human Evaluation Criteria**

**Realism**: Does the generated image look realistic?**Coherence**: Is the generated image consistent and free of artifacts?**Overall Quality**: How does the generated image compare to real images?

### 10.5.3 Evaluating Diversity and Creativity

**Example: Evaluating Diversity**

`# Define a set of inputs with slight variations`

inputs = [

random_noise[0],

random_noise[1],

random_noise[2],

]

# Generate and plot outputs for each input

plt.figure(figsize=(12, 4))

for i, input_data in enumerate(inputs):

step_encodings = create_step_encodings(1, d_model)

output = diffusion_model.predict([np.expand_dims(input_data, axis=0), step_encodings])[0]

plt.subplot(1, 3, i + 1)

plt.imshow((output * 0.5) + 0.5)

plt.axis('off')

plt.title(f'Generated Image {i+1}')

plt.show()

**Summary**