diffusion_model_book_1_5_1_langevin_monte_carlo.ipynb

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            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "41f4c28b7a2043e8b9785263f7e85e39": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "DescriptionStyleModel",
          "model_module_version": "1.5.0",
          "state": {
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "DescriptionStyleModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "StyleView",
            "description_width": ""
          }
        }
      }
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/shu65/diffusion-model-book/blob/main/diffusion_model_book_1_5_1_langevin_monte_carlo.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": "j8oE3NQcYmby"
      },
      "outputs": [],
      "source": [
        "%matplotlib inline\n",
        "import numpy as np\n",
        "import torch\n",
        "import matplotlib.pyplot as plt\n",
        "from tqdm import tqdm_notebook as tqdm"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def log_p_dist(x):\n",
        "  dist0 = torch.distributions.MultivariateNormal(torch.tensor([-2, -2]), torch.eye(2))\n",
        "  p0 = torch.exp(dist0.log_prob(x))\n",
        "  dist1 = torch.distributions.MultivariateNormal(torch.tensor([2, 2]), torch.eye(2))\n",
        "  p1 = torch.exp(dist1.log_prob(x))\n",
        "  return torch.log((p0 + p1)/2.0)"
      ],
      "metadata": {
        "id": "vvXGQ4FzaBIT"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "r = np.linspace(-5, 5, 1000)\n",
        "x0, x1 = np.meshgrid(r, r)\n",
        "x = torch.tensor(np.vstack([x0.flatten(), x1.flatten()]).T)\n",
        "\n",
        "log_p = log_p_dist(x)\n",
        "p = torch.exp(log_p)\n",
        "plt.pcolormesh(x0, x1, p.reshape(x0.shape), cmap='viridis')\n",
        "plt.gca().set_aspect('equal', adjustable='box')\n",
        "plt.xlim([-5, 5])\n",
        "plt.ylim([-5, 5])\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "6kiGPZ7waDe3",
        "outputId": "297fcdd6-b35f-49c2-cbe5-d413cd240d90"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def langevin_monte_carlo_algorithm(log_p_dist, n_samples=100000, alpha=0.001, K=1000):\n",
        "    x0 = torch.randn(n_samples, 2)\n",
        "    x_k = x0\n",
        "    for i in tqdm(range(K+1)):\n",
        "        x_k.requires_grad_()\n",
        "        log_p = log_p_dist(x_k)\n",
        "        score = torch.autograd.grad(log_p.sum(), x_k)[0]\n",
        "        with torch.no_grad():\n",
        "          u_k = torch.randn(n_samples, 2)\n",
        "          x_k = x_k + alpha * score + np.sqrt(2 * alpha) * u_k\n",
        "    return x_k"
      ],
      "metadata": {
        "id": "gfdHf-Aw-F_a"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "samples_1em1 = langevin_monte_carlo_algorithm(log_p_dist, alpha=1e-1).detach().numpy()\n",
        "\n",
        "plt.hist2d(samples_1em1[:,0], samples_1em1[:,1], range=((-5, 5), (-5, 5)), cmap='viridis', rasterized=False, bins=100, density=True)\n",
        "plt.gca().set_aspect('equal', adjustable='box')\n",
        "plt.xlim([-5, 5])\n",
        "plt.ylim([-5, 5])\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351,
          "referenced_widgets": [
            "8c326619a0ac418f8e80aa801b61b781",
            "abe2012f60704febbedafb3d962348ba",
            "ca1bc361842540d594117d08ffe2357c",
            "b39c79a5a26c45d0a25a8cffb74e8f67",
            "357a5a6aefe6440a88dd9da145bcfa49",
            "c477881501994dc29040829a62941390",
            "e57d38392455438eb3e1d21869dc954d",
            "810df2f62c9d4645bfcb693811ecd1f2",
            "670d289da45148d9bde9fa31f5af80fb",
            "5bb1e15b01264c2fb7273d3d178dd5e3",
            "86060565ade94bfd90447b2c31308b59"
          ]
        },
        "id": "Gul5CPl1csz8",
        "outputId": "ca47a54c-22fb-41b9-ebec-9a24c94e6fed"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-4-2b227ecd6a2d>:4: TqdmDeprecationWarning: This function will be removed in tqdm==5.0.0\n",
            "Please use `tqdm.notebook.tqdm` instead of `tqdm.tqdm_notebook`\n",
            "  for i in tqdm(range(K+1)):\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  0%|          | 0/1001 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "8c326619a0ac418f8e80aa801b61b781"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "samples_1em5 = langevin_monte_carlo_algorithm(log_p_dist, alpha=1e-5).detach().numpy()\n",
        "\n",
        "plt.hist2d(samples_1em5[:,0], samples_1em5[:,1], range=((-5, 5), (-5, 5)), cmap='viridis', rasterized=False, bins=100, density=True)\n",
        "plt.gca().set_aspect('equal', adjustable='box')\n",
        "plt.xlim([-5, 5])\n",
        "plt.ylim([-5, 5])\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351,
          "referenced_widgets": [
            "204e7e0ed0a54bb0b5eba169bb6bcec9",
            "a3f9e9ee9de04a578c3167e140844033",
            "e029ee3fee7d448bb687c041204b3126",
            "251eec4a9d4242f58dbea5554ffd9246",
            "69be29c0647f4312a132a71310a95304",
            "fa401337adb84738be1fcbf61583dc3f",
            "611a88637e2d400593a82f606b51ce90",
            "c14ffb25b7be413884e184fca25e852a",
            "5bc0ee2f0ad446c093ebf242ef11d08e",
            "b895f41a82614b168455ec9baa4f9219",
            "41f4c28b7a2043e8b9785263f7e85e39"
          ]
        },
        "id": "I_Qij9xTfL-s",
        "outputId": "ff59cf3e-8669-4a24-c36a-a02c2ad8a816"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-4-2b227ecd6a2d>:4: TqdmDeprecationWarning: This function will be removed in tqdm==5.0.0\n",
            "Please use `tqdm.notebook.tqdm` instead of `tqdm.tqdm_notebook`\n",
            "  for i in tqdm(range(K+1)):\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  0%|          | 0/1001 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "204e7e0ed0a54bb0b5eba169bb6bcec9"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}