diffusion_model_image_generation.ipynb

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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "gpuType": "T4",
      "authorship_tag": "ABX9TyOOV+23zkr5Y8GY7uNUncj+",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/karthiknadar1204/generative_deep_learning/blob/main/diffusion_model_image_generation.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "FzBFKZKXE_F6"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.style.use(\"seaborn-v0_8-colorblind\")\n",
        "\n",
        "import math\n",
        "\n",
        "import tensorflow as tf\n",
        "from tensorflow.keras import (\n",
        "    layers,\n",
        "    models,\n",
        "    optimizers,\n",
        "    utils,\n",
        "    callbacks,\n",
        "    metrics,\n",
        "    losses,\n",
        "    activations,\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "IMAGE_SIZE = 64\n",
        "BATCH_SIZE = 64\n",
        "DATASET_REPETITIONS = 5\n",
        "LOAD_MODEL = False\n",
        "\n",
        "NOISE_EMBEDDING_SIZE = 32\n",
        "PLOT_DIFFUSION_STEPS = 20\n",
        "\n",
        "# optimization\n",
        "EMA = 0.999\n",
        "LEARNING_RATE = 1e-3\n",
        "WEIGHT_DECAY = 1e-4\n",
        "EPOCHS = 50"
      ],
      "metadata": {
        "id": "7676A3WMWanN"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install -q kaggle\n",
        "! mkdir ~/.kaggle\n",
        "! cp kaggle.json ~/.kaggle/\n",
        "!chmod 600 /root/.kaggle/kaggle.json\n",
        "!kaggle datasets download -d nunenuh/pytorch-challange-flower-dataset\n",
        "!unzip \"/content/pytorch-challange-flower-dataset.zip\" -d \"/content/dataset/\""
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uKoRBuzuWrpW",
        "outputId": "1b0c11ed-4173-4678-b5bc-19e180f078ea"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[1;30;43mStreaming output truncated to the last 5000 lines.\u001b[0m\n",
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    },
    {
      "cell_type": "code",
      "source": [
        "!ls /content/dataset/dataset/train\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "n3v0GSSdWrzx",
        "outputId": "25dbb03a-7a58-4f57-be62-c0ada2900368"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1    11  16  20  25  3\t 34  39  43  48  52  57  61  66  70  75  8   84  89  93  98\n",
            "10   12  17  21  26  30  35  4\t 44  49  53  58  62  67  71  76  80  85  9   94  99\n",
            "100  13  18  22  27  31  36  40  45  5\t 54  59  63  68  72  77  81  86  90  95\n",
            "101  14  19  23  28  32  37  41  46  50  55  6\t 64  69  73  78  82  87  91  96\n",
            "102  15  2   24  29  33  38  42  47  51  56  60  65  7\t 74  79  83  88  92  97\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Load the data\n",
        "train_data = utils.image_dataset_from_directory(\n",
        "    \"/content/dataset/dataset/train\",\n",
        "    labels=None,\n",
        "    image_size=(IMAGE_SIZE, IMAGE_SIZE),\n",
        "    batch_size=None,\n",
        "    shuffle=True,\n",
        "    seed=42,\n",
        "    interpolation=\"bilinear\",\n",
        ")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "w8aeT3c4Was7",
        "outputId": "1e8a7f33-24dc-4038-c5c7-0142c34068f7"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Found 6552 files belonging to 1 classes.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Preprocess the data\n",
        "def preprocess(img):\n",
        "    img = tf.cast(img, \"float32\") / 255.0\n",
        "    return img\n",
        "\n",
        "\n",
        "train = train_data.map(lambda x: preprocess(x))\n",
        "train = train.repeat(DATASET_REPETITIONS)\n",
        "train = train.batch(BATCH_SIZE, drop_remainder=True)"
      ],
      "metadata": {
        "id": "suXTQIjUWayQ"
      },
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Show some items of clothing from the training set\n",
        "train_sample = sample_batch(train)\n",
        "display(train_sample)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 180
        },
        "id": "X-d1-Y7LWa3D",
        "outputId": "3c9bf812-cda6-4c31-b7d0-8b5025b0c034"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "name 'sample_batch' is not defined",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-20-bcd48f084399>\u001b[0m in \u001b[0;36m<cell line: 2>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# Show some items of clothing from the training set\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mtrain_sample\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msample_batch\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrain\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mdisplay\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrain_sample\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'sample_batch' is not defined"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def linear_diffusion_schedule(diffusion_times):\n",
        "    min_rate = 0.0001\n",
        "    max_rate = 0.02\n",
        "    betas = min_rate + diffusion_times * (max_rate - min_rate)\n",
        "    alphas = 1 - betas\n",
        "    alpha_bars = tf.math.cumprod(alphas)\n",
        "    signal_rates = tf.sqrt(alpha_bars)\n",
        "    noise_rates = tf.sqrt(1 - alpha_bars)\n",
        "    return noise_rates, signal_rates"
      ],
      "metadata": {
        "id": "Vo17KvJyWa7e"
      },
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def cosine_diffusion_schedule(diffusion_times):\n",
        "    signal_rates = tf.cos(diffusion_times * math.pi / 2)\n",
        "    noise_rates = tf.sin(diffusion_times * math.pi / 2)\n",
        "    return noise_rates, signal_rates"
      ],
      "metadata": {
        "id": "WeGublIeWa_l"
      },
      "execution_count": 22,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def offset_cosine_diffusion_schedule(diffusion_times):\n",
        "    min_signal_rate = 0.02\n",
        "    max_signal_rate = 0.95\n",
        "    start_angle = tf.acos(max_signal_rate)\n",
        "    end_angle = tf.acos(min_signal_rate)\n",
        "\n",
        "    diffusion_angles = start_angle + diffusion_times * (end_angle - start_angle)\n",
        "\n",
        "    signal_rates = tf.cos(diffusion_angles)\n",
        "    noise_rates = tf.sin(diffusion_angles)\n",
        "\n",
        "    return noise_rates, signal_rates"
      ],
      "metadata": {
        "id": "XZH4fAP6WbEr"
      },
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "T = 1000\n",
        "diffusion_times = tf.convert_to_tensor([x / T for x in range(T)])\n",
        "linear_noise_rates, linear_signal_rates = linear_diffusion_schedule(\n",
        "    diffusion_times\n",
        ")\n",
        "cosine_noise_rates, cosine_signal_rates = cosine_diffusion_schedule(\n",
        "    diffusion_times\n",
        ")\n",
        "(\n",
        "    offset_cosine_noise_rates,\n",
        "    offset_cosine_signal_rates,\n",
        ") = offset_cosine_diffusion_schedule(diffusion_times)"
      ],
      "metadata": {
        "id": "epLVwkoBiWDI"
      },
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(\n",
        "    diffusion_times, linear_signal_rates**2, linewidth=1.5, label=\"linear\"\n",
        ")\n",
        "plt.plot(\n",
        "    diffusion_times, cosine_signal_rates**2, linewidth=1.5, label=\"cosine\"\n",
        ")\n",
        "plt.plot(\n",
        "    diffusion_times,\n",
        "    offset_cosine_signal_rates**2,\n",
        "    linewidth=1.5,\n",
        "    label=\"offset_cosine\",\n",
        ")\n",
        "\n",
        "plt.xlabel(\"t/T\", fontsize=12)\n",
        "plt.ylabel(r\"$\\bar{\\alpha_t}$ (signal)\", fontsize=12)\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 453
        },
        "id": "kKY8rHYYiWLb",
        "outputId": "183f2e63-f807-41ee-ac11-6e11a36a953b"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(\n",
        "    diffusion_times, linear_noise_rates**2, linewidth=1.5, label=\"linear\"\n",
        ")\n",
        "plt.plot(\n",
        "    diffusion_times, cosine_noise_rates**2, linewidth=1.5, label=\"cosine\"\n",
        ")\n",
        "plt.plot(\n",
        "    diffusion_times,\n",
        "    offset_cosine_noise_rates**2,\n",
        "    linewidth=1.5,\n",
        "    label=\"offset_cosine\",\n",
        ")\n",
        "\n",
        "plt.xlabel(\"t/T\", fontsize=12)\n",
        "plt.ylabel(r\"$1-\\bar{\\alpha_t}$ (noise)\", fontsize=12)\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 453
        },
        "id": "NeE0Pc68imiV",
        "outputId": "526aed85-7e97-4b9b-89d0-331f217687ee"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def sinusoidal_embedding(x):\n",
        "    frequencies = tf.exp(\n",
        "        tf.linspace(\n",
        "            tf.math.log(1.0),\n",
        "            tf.math.log(1000.0),\n",
        "            NOISE_EMBEDDING_SIZE // 2,\n",
        "        )\n",
        "    )\n",
        "    angular_speeds = 2.0 * math.pi * frequencies\n",
        "    embeddings = tf.concat(\n",
        "        [tf.sin(angular_speeds * x), tf.cos(angular_speeds * x)], axis=3\n",
        "    )\n",
        "    return embeddings"
      ],
      "metadata": {
        "id": "4g5ltKbhimpF"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "embedding_list = []\n",
        "for y in np.arange(0, 1, 0.01):\n",
        "    embedding_list.append(sinusoidal_embedding(np.array([[[[y]]]]))[0][0][0])\n",
        "embedding_array = np.array(np.transpose(embedding_list))\n",
        "fig, ax = plt.subplots()\n",
        "ax.set_xticks(\n",
        "    np.arange(0, 100, 10), labels=np.round(np.arange(0.0, 1.0, 0.1), 1)\n",
        ")\n",
        "ax.set_ylabel(\"embedding dimension\", fontsize=8)\n",
        "ax.set_xlabel(\"noise variance\", fontsize=8)\n",
        "plt.pcolor(embedding_array, cmap=\"coolwarm\")\n",
        "plt.colorbar(orientation=\"horizontal\", label=\"embedding value\")\n",
        "ax.imshow(embedding_array, interpolation=\"nearest\", origin=\"lower\")\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "eSKMmxEai2Ea"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def ResidualBlock(width):\n",
        "    def apply(x):\n",
        "        input_width = x.shape[3]\n",
        "        if input_width == width:\n",
        "            residual = x\n",
        "        else:\n",
        "            residual = layers.Conv2D(width, kernel_size=1)(x)\n",
        "        x = layers.BatchNormalization(center=False, scale=False)(x)\n",
        "        x = layers.Conv2D(\n",
        "            width, kernel_size=3, padding=\"same\", activation=activations.swish\n",
        "        )(x)\n",
        "        x = layers.Conv2D(width, kernel_size=3, padding=\"same\")(x)\n",
        "        x = layers.Add()([x, residual])\n",
        "        return x\n",
        "\n",
        "    return apply\n",
        "\n",
        "\n",
        "def DownBlock(width, block_depth):\n",
        "    def apply(x):\n",
        "        x, skips = x\n",
        "        for _ in range(block_depth):\n",
        "            x = ResidualBlock(width)(x)\n",
        "            skips.append(x)\n",
        "        x = layers.AveragePooling2D(pool_size=2)(x)\n",
        "        return x\n",
        "\n",
        "    return apply\n",
        "\n",
        "\n",
        "def UpBlock(width, block_depth):\n",
        "    def apply(x):\n",
        "        x, skips = x\n",
        "        x = layers.UpSampling2D(size=2, interpolation=\"bilinear\")(x)\n",
        "        for _ in range(block_depth):\n",
        "            x = layers.Concatenate()([x, skips.pop()])\n",
        "            x = ResidualBlock(width)(x)\n",
        "        return x\n",
        "\n",
        "    return apply"
      ],
      "metadata": {
        "id": "JQ4y6Og3i2Kv"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Build the U-Net\n",
        "\n",
        "noisy_images = layers.Input(shape=(IMAGE_SIZE, IMAGE_SIZE, 3))\n",
        "x = layers.Conv2D(32, kernel_size=1)(noisy_images)\n",
        "\n",
        "noise_variances = layers.Input(shape=(1, 1, 1))\n",
        "noise_embedding = layers.Lambda(sinusoidal_embedding)(noise_variances)\n",
        "noise_embedding = layers.UpSampling2D(size=IMAGE_SIZE, interpolation=\"nearest\")(\n",
        "    noise_embedding\n",
        ")\n",
        "\n",
        "x = layers.Concatenate()([x, noise_embedding])\n",
        "\n",
        "skips = []\n",
        "\n",
        "x = DownBlock(32, block_depth=2)([x, skips])\n",
        "x = DownBlock(64, block_depth=2)([x, skips])\n",
        "x = DownBlock(96, block_depth=2)([x, skips])\n",
        "\n",
        "x = ResidualBlock(128)(x)\n",
        "x = ResidualBlock(128)(x)\n",
        "\n",
        "x = UpBlock(96, block_depth=2)([x, skips])\n",
        "x = UpBlock(64, block_depth=2)([x, skips])\n",
        "x = UpBlock(32, block_depth=2)([x, skips])\n",
        "\n",
        "x = layers.Conv2D(3, kernel_size=1, kernel_initializer=\"zeros\")(x)\n",
        "\n",
        "unet = models.Model([noisy_images, noise_variances], x, name=\"unet\")"
      ],
      "metadata": {
        "id": "jt8iNJjxi2Qc"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class DiffusionModel(models.Model):\n",
        "    def __init__(self):\n",
        "        super().__init__()\n",
        "\n",
        "        self.normalizer = layers.Normalization()\n",
        "        self.network = unet\n",
        "        self.ema_network = models.clone_model(self.network)\n",
        "        self.diffusion_schedule = offset_cosine_diffusion_schedule\n",
        "\n",
        "    def compile(self, **kwargs):\n",
        "        super().compile(**kwargs)\n",
        "        self.noise_loss_tracker = metrics.Mean(name=\"n_loss\")\n",
        "\n",
        "    @property\n",
        "    def metrics(self):\n",
        "        return [self.noise_loss_tracker]\n",
        "\n",
        "    def denormalize(self, images):\n",
        "        images = self.normalizer.mean + images * self.normalizer.variance**0.5\n",
        "        return tf.clip_by_value(images, 0.0, 1.0)\n",
        "\n",
        "    def denoise(self, noisy_images, noise_rates, signal_rates, training):\n",
        "        if training:\n",
        "            network = self.network\n",
        "        else:\n",
        "            network = self.ema_network\n",
        "        pred_noises = network(\n",
        "            [noisy_images, noise_rates**2], training=training\n",
        "        )\n",
        "        pred_images = (noisy_images - noise_rates * pred_noises) / signal_rates\n",
        "\n",
        "        return pred_noises, pred_images\n",
        "\n",
        "    def reverse_diffusion(self, initial_noise, diffusion_steps):\n",
        "        num_images = initial_noise.shape[0]\n",
        "        step_size = 1.0 / diffusion_steps\n",
        "        current_images = initial_noise\n",
        "        for step in range(diffusion_steps):\n",
        "            diffusion_times = tf.ones((num_images, 1, 1, 1)) - step * step_size\n",
        "            noise_rates, signal_rates = self.diffusion_schedule(diffusion_times)\n",
        "            pred_noises, pred_images = self.denoise(\n",
        "                current_images, noise_rates, signal_rates, training=False\n",
        "            )\n",
        "            next_diffusion_times = diffusion_times - step_size\n",
        "            next_noise_rates, next_signal_rates = self.diffusion_schedule(\n",
        "                next_diffusion_times\n",
        "            )\n",
        "            current_images = (\n",
        "                next_signal_rates * pred_images + next_noise_rates * pred_noises\n",
        "            )\n",
        "        return pred_images\n",
        "\n",
        "    def generate(self, num_images, diffusion_steps, initial_noise=None):\n",
        "        if initial_noise is None:\n",
        "            initial_noise = tf.random.normal(\n",
        "                shape=(num_images, IMAGE_SIZE, IMAGE_SIZE, 3)\n",
        "            )\n",
        "        generated_images = self.reverse_diffusion(\n",
        "            initial_noise, diffusion_steps\n",
        "        )\n",
        "        generated_images = self.denormalize(generated_images)\n",
        "        return generated_images\n",
        "\n",
        "    def train_step(self, images):\n",
        "        images = self.normalizer(images, training=True)\n",
        "        noises = tf.random.normal(shape=(BATCH_SIZE, IMAGE_SIZE, IMAGE_SIZE, 3))\n",
        "\n",
        "        diffusion_times = tf.random.uniform(\n",
        "            shape=(BATCH_SIZE, 1, 1, 1), minval=0.0, maxval=1.0\n",
        "        )\n",
        "        noise_rates, signal_rates = self.diffusion_schedule(diffusion_times)\n",
        "\n",
        "        noisy_images = signal_rates * images + noise_rates * noises\n",
        "\n",
        "        with tf.GradientTape() as tape:\n",
        "            # train the network to separate noisy images to their components\n",
        "            pred_noises, pred_images = self.denoise(\n",
        "                noisy_images, noise_rates, signal_rates, training=True\n",
        "            )\n",
        "\n",
        "            noise_loss = self.loss(noises, pred_noises)  # used for training\n",
        "\n",
        "        gradients = tape.gradient(noise_loss, self.network.trainable_weights)\n",
        "        self.optimizer.apply_gradients(\n",
        "            zip(gradients, self.network.trainable_weights)\n",
        "        )\n",
        "\n",
        "        self.noise_loss_tracker.update_state(noise_loss)\n",
        "\n",
        "        for weight, ema_weight in zip(\n",
        "            self.network.weights, self.ema_network.weights\n",
        "        ):\n",
        "            ema_weight.assign(EMA * ema_weight + (1 - EMA) * weight)\n",
        "\n",
        "        return {m.name: m.result() for m in self.metrics}\n",
        "\n",
        "    def test_step(self, images):\n",
        "        images = self.normalizer(images, training=False)\n",
        "        noises = tf.random.normal(shape=(BATCH_SIZE, IMAGE_SIZE, IMAGE_SIZE, 3))\n",
        "        diffusion_times = tf.random.uniform(\n",
        "            shape=(BATCH_SIZE, 1, 1, 1), minval=0.0, maxval=1.0\n",
        "        )\n",
        "        noise_rates, signal_rates = self.diffusion_schedule(diffusion_times)\n",
        "        noisy_images = signal_rates * images + noise_rates * noises\n",
        "        pred_noises, pred_images = self.denoise(\n",
        "            noisy_images, noise_rates, signal_rates, training=False\n",
        "        )\n",
        "        noise_loss = self.loss(noises, pred_noises)\n",
        "        self.noise_loss_tracker.update_state(noise_loss)\n",
        "\n",
        "        return {m.name: m.result() for m in self.metrics}"
      ],
      "metadata": {
        "id": "8cBKhqqiWbLb"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "ddm = DiffusionModel()\n",
        "ddm.normalizer.adapt(train)"
      ],
      "metadata": {
        "id": "EIMFq9oQWbPH"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "if LOAD_MODEL:\n",
        "    ddm.built = True\n",
        "    ddm.load_weights(\"./checkpoint/checkpoint.ckpt\")"
      ],
      "metadata": {
        "id": "DA5GK4yrYX7g"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "ddm.compile(\n",
        "    optimizer=optimizers.experimental.AdamW(\n",
        "        learning_rate=LEARNING_RATE, weight_decay=WEIGHT_DECAY\n",
        "    ),\n",
        "    loss=losses.mean_absolute_error,\n",
        ")"
      ],
      "metadata": {
        "id": "_2dNESqfYemd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# run training and plot generated images periodically\n",
        "model_checkpoint_callback = callbacks.ModelCheckpoint(\n",
        "    filepath=\"./checkpoint/checkpoint.ckpt\",\n",
        "    save_weights_only=True,\n",
        "    save_freq=\"epoch\",\n",
        "    verbose=0,\n",
        ")\n",
        "\n",
        "tensorboard_callback = callbacks.TensorBoard(log_dir=\"./logs\")\n",
        "\n",
        "\n",
        "class ImageGenerator(callbacks.Callback):\n",
        "    def __init__(self, num_img):\n",
        "        self.num_img = num_img\n",
        "\n",
        "    def on_epoch_end(self, epoch, logs=None):\n",
        "        generated_images = self.model.generate(\n",
        "            num_images=self.num_img,\n",
        "            diffusion_steps=PLOT_DIFFUSION_STEPS,\n",
        "        ).numpy()\n",
        "        display(\n",
        "            generated_images,\n",
        "            save_to=\"./output/generated_img_%03d.png\" % (epoch),\n",
        "        )\n",
        "\n",
        "\n",
        "image_generator_callback = ImageGenerator(num_img=10)\n",
        "\n",
        "ddm.fit(\n",
        "    train,\n",
        "    epochs=EPOCHS,\n",
        "    callbacks=[\n",
        "        model_checkpoint_callback,\n",
        "        tensorboard_callback,\n",
        "        image_generator_callback,\n",
        "    ],\n",
        ")"
      ],
      "metadata": {
        "id": "f15DLR0fYesO"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Generate some novel images of flowers\n",
        "generated_images = ddm.generate(num_images=10, diffusion_steps=20).numpy()\n",
        "display(generated_images)"
      ],
      "metadata": {
        "id": "OiSUn2ZwYexq"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# View improvement over greater number of diffusion steps\n",
        "for diffusion_steps in list(np.arange(1, 6, 1)) + [20] + [100]:\n",
        "    tf.random.set_seed(42)\n",
        "    generated_images = ddm.generate(\n",
        "        num_images=10,\n",
        "        diffusion_steps=diffusion_steps,\n",
        "    ).numpy()\n",
        "    display(generated_images)"
      ],
      "metadata": {
        "id": "Gj5x5xwNYe2v"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Interpolation between two points in the latent space\n",
        "tf.random.set_seed(100)\n",
        "\n",
        "\n",
        "def spherical_interpolation(a, b, t):\n",
        "    return np.sin(t * math.pi / 2) * a + np.cos(t * math.pi / 2) * b\n",
        "\n",
        "\n",
        "for i in range(5):\n",
        "    a = tf.random.normal(shape=(IMAGE_SIZE, IMAGE_SIZE, 3))\n",
        "    b = tf.random.normal(shape=(IMAGE_SIZE, IMAGE_SIZE, 3))\n",
        "    initial_noise = np.array(\n",
        "        [spherical_interpolation(a, b, t) for t in np.arange(0, 1.1, 0.1)]\n",
        "    )\n",
        "    generated_images = ddm.generate(\n",
        "        num_images=2, diffusion_steps=20, initial_noise=initial_noise\n",
        "    ).numpy()\n",
        "    display(generated_images, n=11)"
      ],
      "metadata": {
        "id": "bBNLLNE0Ye7f"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}