{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "8wN_a5HUpXq3" }, "source": [ "# Acknowledgement\n", "\n", "Parts of this pset were inspired by\n", "* Berkeley CS294-158, taught by Pieter Abbeel, Wilson Yan, Kevin Frans, and Philipp Wu;\n", "* MIT 6.S184/6.S975, taught by Peter Holderrieth and Ezra Erives;\n", "* The [blog post](https://lilianweng.github.io/posts/2021-07-11-diffusion-models/) about diffusion models by Lilian Weng.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Submission Guideline for Part 2\n", "\n", "Please include your answer to all problems, including formulas, proofs, and the figures generated in each problem, excluding code. You are required to submit the (single) pdf and all (four) notebooks (one for each problem) with your code and running outputs. Do not include code in the pdf file. \n", "\n", "Specifically, for Problem 2 in this notebook, the pdf should contain:\n", "- The generated figures `results/p2_train_plot.png` and `results/p2_toy_samples.png`" ] }, { "cell_type": "markdown", "metadata": { "id": "9f3Fo0bam8QD" }, "source": [ "# Problem 2: Training Diffusion Models on a Toy Dataset\n", "In this problem, we will write the code for training and sampling from a diffusion model on a 2D toy dataset. This part requires GPUs--you can use Google Colab for GPU access. To work on this notebook in Google Colab, copy the `pset-5` directory to your Google Drive and open this notebook. Then, start working on a GPU machine with `Runtime -> Change runtime type -> T4 GPU`." ] }, { "cell_type": "markdown", "metadata": { "id": "2DZudkhDhma4" }, "source": [ "## Data Generation and Visualization" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 430 }, "id": "FfknAoMdnOdI", "outputId": "936110ad-e445-4ee6-dca1-7daf7f25e13e" }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import make_s_curve\n", "import matplotlib.pyplot as plt\n", "\n", "def toy_2d_data(n=100000):\n", " x, _ = make_s_curve(n, noise=0.1)\n", " x = x[:, [0, 2]]\n", " return x.astype('float32')\n", "\n", "def visualize_toy_2d_dataset():\n", " data = toy_2d_data()\n", " plt.figure()\n", " plt.scatter(data[:, 0], data[:, 1])\n", " plt.show()\n", "\n", "visualize_toy_2d_dataset()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Training and Sampling of Diffusion Models" ] }, { "cell_type": "markdown", "metadata": { "id": "E1G44tSboPBD" }, "source": [ "For code simplicity, we will train a continuous-time variant of the diffusion prompt. In practice training objectives and code between discrete-time and continuous-time diffusion models are similar.\n", "\n", "Given a data element $x$ and neural net $f_\\theta(x, t)$, implement the following diffusion training steps:\n", "\n", "0. Construct a class `Diffusion`\n", "1. Sample the diffusion timestep: $t \\sim \\text{Uniform}(0, 1)$\n", "2. Compute the noise-strength following a cosine schedule: $\\alpha_t = \\cos\\left(\\frac{\\pi}{2}t\\right), \\sigma_t = \\sin\\left(\\frac{\\pi}{2}t\\right)$\n", "3. Sample noise $\\epsilon \\sim N(0,I)$ (same shape as $x$) and cmpute noised $x_t = \\alpha_t x + \\sigma_t \\epsilon$\n", "4. Estimate $\\hat{\\epsilon} = f_\\theta(x_t, t)$\n", "5. Optimize the loss $L = \\lVert \\epsilon - \\hat{\\epsilon} \\rVert_2^2$. Here, it suffices to just take the mean over all dimensions.\n", "\n", "Note that for the case of continuous-time diffusion, the forward process is $x_{0\\to1}$ and reverse process is $x_{1\\to0}$\n", "\n", "Use an MLP for $f_\\theta$ to optimize the loss. You may find the following details helpful.\n", "* Normalize the data using mean and std computed from the train dataset\n", "* Train 100 epochs, batch size 1024, Adam with LR 1e-3 (100 warmup steps, cosine decay to 0)\n", "* MLP with 4 hidden layers and hidden size 64\n", "* Condition on t by concatenating it with input x (i.e. 2D x + 1D t = 3D cat(x, t))\n", "* Training 100 epochs takes about 2 minutes on the Google Colab T4 GPU.\n", "\n", "\n", "To sample, implement the standard DDPM sampler. You may find the equation from the [DDIM paper](https://arxiv.org/pdf/2010.02502.pdf) helpful, rewritten and re-formatted here for convenience.\n", "$$x_{t-1} = \\alpha_{t-1}\\left(\\frac{x_t - \\sigma_t\\hat{\\epsilon}}{\\alpha_t}\\right) + \\sqrt{\\sigma_{t-1}^2 - \\eta_t^2}\\hat{\\epsilon} + \\eta_t\\epsilon_t$$\n", "where $\\epsilon_t \\sim N(0, I)$ is random Gaussian noise. For DDPM, let\n", "$$\\eta_t = \\sigma_{t-1}/\\sigma_t\\sqrt{1 - \\alpha_t^2/\\alpha_{t-1}^2}$$\n", "*Note*: As a sanity check, when $\\eta_t$ follows the DDPM setting as shown above, the resulted coefficient of $x_t$ and $\\hat{\\epsilon}$ should be the same as $A'$ and $B'$ you derived in Problem 1.2 (6) where $\\alpha_t$ here corresponds to $\\bar{\\alpha_t}$ in Problem 1.\n", "\n", "To run the reverse process, start from $x_1 \\sim N(0, I)$. Then perform `num_steps` DDPM updates (a hyperparameter), pseudocode below.\n", "```\n", "ts = linspace(1 - 1e-4, 1e-4, num_steps + 1)\n", "x = sample_normal\n", "for i in range(num_steps):\n", " t = ts[i]\n", " tm1 = ts[i + 1]\n", " eps_hat = model(x, t)\n", " x = DDPM_UPDATE(x, eps_hat, t, tm1)\n", "return x\n", "```\n", "*Note*: \n", "* If you encounter NaNs, you may need to clip $\\sigma_{t-1}^2 - \\eta_t^2$ to 0 if it goes negative, as machine precision issues can make it a very small negative number (e.g. -1e-12) if its too close to 0\n", "* For debugging, you can start with trying small number of epochs. To debug your training code, you can check whether the training and testing losses decrease properly. To debug your sampling code, you can check whether the generated distribution is close to the S-shape target distribution with large `num_steps`.\n", "* To check your answer, the final text loss is roughly around 0.4." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "id": "3vzaYVRdoQzE" }, "outputs": [], "source": [ "import torch\n", "import torch.nn as nn\n", "import math\n", "import numpy as np\n", "\n", "class Diffusion:\n", " def __init__(self, model, data_shape):\n", " \"\"\"\n", " model: neural network to estimate eps_hat (MLP in this problem)\n", " data_shape: size of the input data, (2,) in this case\n", " \"\"\"\n", " self.model = model\n", " self.data_shape = data_shape\n", "\n", " def loss(self, x):\n", " \"\"\"\n", " x: the input data (without adding noise) from the dataloader\n", " Return:\n", " The loss (as a scalar averaged over all data in the batch)\n", " \"\"\"\n", " raise NotImplementedError(\"Please implement this\")\n", "\n", " @torch.no_grad()\n", " def sample(self, n, num_steps):\n", " \"\"\"\n", " n: number of samples to generate\n", " num_steps: number of steps in the diffusion sampling\n", " Return:\n", " The generated sample. Tensor with shape (n, *self.data_shape)\n", " \"\"\"\n", " raise NotImplementedError(\"Please implement this\")\n", "\n", " def __getattr__(self, name):\n", " if name in ['train', 'eval', 'parameters', 'state_dict', 'load_state_dict']:\n", " return getattr(self.model, name)\n", " return self.__getattribute__(name)\n", "\n", "\n", "class MLP(nn.Module):\n", " def __init__(self, input_dim, hidden_dim, n_hidden_layers, timestep_dim=1):\n", " super().__init__()\n", " self.timestep_dim = timestep_dim\n", " prev_dim = input_dim + timestep_dim\n", " net = []\n", " dims = [hidden_dim] * n_hidden_layers + [input_dim]\n", " for i, dim in enumerate(dims):\n", " net.append(nn.Linear(prev_dim, dim))\n", " if i < len(dims) - 1:\n", " net.append(nn.ReLU())\n", " prev_dim = dim\n", " self.net = nn.Sequential(*net)\n", "\n", " def forward(self, x, t):\n", " x = torch.cat([x, t[:, None]], dim=1)\n", " return self.net(x)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "id": "ksapA-iaoQgU" }, "outputs": [], "source": [ "import torch.optim as optim\n", "from torch.utils.data import DataLoader\n", "from tqdm import tqdm\n", "\n", "def train(model, train_loader, optimizer, scheduler):\n", " \"\"\"\n", " model: model to train, the Diffusion class in this case.\n", " train_loader: dataloader for the train_data after normalization\n", " optimizer: use torch.optim.Adam\n", " scheduler: use optim.lr_scheduler.LambdaLR(\n", " optimizer,\n", " lr_lambda=lambda step: get_lr(step, total_steps, warmup_steps, use_cos_decay)\n", " )\n", " Return:\n", " Tensor with train loss of each batch\n", " \"\"\"\n", " raise NotImplementedError(\"Please implement this\")\n", "\n", "@torch.no_grad()\n", "def eval_loss(model, data_loader):\n", " \"\"\"\n", " model: model to train, the Diffusion class in this case.\n", " data_loader: dataloader for the test_data after normalization\n", " Return:\n", " Scalar with the average test loss of each batch\n", " \"\"\"\n", " raise NotImplementedError(\"Please implement this\")\n", "\n", "def get_lr(step, total_steps, warmup_steps, use_cos_decay):\n", " \"\"\"\n", " Function that returns the learning rate for the specific step, used in defining the scheduler:\n", " scheduler = optim.lr_scheduler.LambdaLR(\n", " optimizer,\n", " lr_lambda=lambda step: get_lr(step, total_steps, warmup_steps, use_cos_decay)\n", " )\n", " \"\"\"\n", " raise NotImplementedError(\"Please implement this\")\n", "\n", "def train_epochs(model, train_loader, test_loader, train_args):\n", " \"\"\"\n", " model: model to train, the Diffusion class in this case.\n", " train_loader: dataloader for the train_data after normalization\n", " test_loader: dataloader for the test_data after normalization\n", " Return:\n", " Two np.array for all the train losses and test losses at each step\n", " \"\"\"\n", " epochs, lr = train_args['epochs'], train_args['lr']\n", " warmup_steps = train_args.get('warmup', 0)\n", " use_cos_decay = train_args.get('use_cos_decay', False)\n", " raise NotImplementedError(\"Please implement this\")\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "id": "bbr4DxGGoQdM" }, "outputs": [], "source": [ "import torch.utils.data as data\n", "\n", "def toy_diffusion(train_data, test_data):\n", " \"\"\"\n", " train_data: A (100000, 2) numpy array of 2D points\n", " test_data: A (10000, 2) numpy array of 2D points\n", "\n", " Returns\n", " - a (# of training iterations,) numpy array of train losses evaluated every minibatch\n", " - a (# of num_epochs + 1,) numpy array of test losses evaluated at the start of training and the end of every epoch\n", " - a numpy array of size (9, 2000, 2) of samples drawn from your model.\n", " Draw 2000 samples for each of 9 different number of diffusion sampling steps\n", " of evenly logarithmically spaced integers 1 to 512\n", " hint: np.power(2, np.linspace(0, 9, 9)).astype(int)\n", " \"\"\"\n", " raise NotImplementedError(\"Please implement this\")\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "id": "YQWzFjaqrDks" }, "outputs": [], "source": [ "import os\n", "from os.path import exists, dirname\n", "\n", "def savefig(fname: str, show_figure: bool = True) -> None:\n", " if not exists(dirname(fname)):\n", " os.makedirs(dirname(fname))\n", " plt.tight_layout()\n", " plt.savefig(fname)\n", " if show_figure:\n", " plt.show()\n", "\n", "\n", "def save_training_plot(\n", " train_losses: np.ndarray, test_losses: np.ndarray, title: str, fname: str\n", ") -> None:\n", " plt.figure()\n", " n_epochs = len(test_losses) - 1\n", " x_train = np.linspace(0, n_epochs, len(train_losses))\n", " x_test = np.arange(n_epochs + 1)\n", "\n", " plt.plot(x_train, train_losses, label=\"train loss\")\n", " plt.plot(x_test, test_losses, label=\"test loss\")\n", " plt.legend()\n", " plt.title(title)\n", " plt.xlabel(\"Epoch\")\n", " plt.ylabel(\"NLL\")\n", " savefig(fname)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "id": "35stTh5Zqo89" }, "outputs": [], "source": [ "def save_multi_scatter_2d(data: np.ndarray) -> None:\n", " fig, axs = plt.subplots(3, 3, figsize=(10, 10))\n", " num_steps = np.power(2, np.linspace(0, 9, 9)).astype(int)\n", " for i in range(3):\n", " for j in range(3):\n", " axs[i, j].scatter(data[i * 3 + j, :, 0], data[i * 3 + j, :, 1])\n", " axs[i, j].set_title(f'Steps = {num_steps[i * 3 + j]}')\n", " savefig(\"results/p2_toy_samples.png\")\n", "\n", "\n", "def toy_save_results(fn):\n", " train_data = toy_2d_data(n=100000)\n", " test_data = toy_2d_data(n=10000)\n", " train_losses, test_losses, samples = fn(train_data, test_data)\n", "\n", " print(f\"Final Test Loss: {test_losses[-1]:.4f}\")\n", "\n", " save_training_plot(\n", " train_losses,\n", " test_losses,\n", " f\"P2 Train Plot\",\n", " f\"results/p2_train_plot.png\"\n", " )\n", "\n", " save_multi_scatter_2d(samples)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "toy_save_results(toy_diffusion)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Submission Guideline for Part 2\n", "\n", "Please include your answer to all problems, including formulas, proofs, and the figures generated in each problem, excluding code. You are required to submit the (single) pdf and all (four) notebooks (one for each problem) with your code and running outputs. Do not include code in the pdf file. \n", "\n", "Specifically, for Problem 2 in this notebook, the pdf should contain:\n", "- The generated figures `results/p2_train_plot.png` and `results/p2_toy_samples.png`" ] } ], "metadata": { "accelerator": "GPU", "colab": { "gpuType": "T4", "provenance": [] }, "kernelspec": { "display_name": "Python 3", "name": "python3" }, "language_info": { "name": "python" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "01d3c22ebc274d04937ff8b3839f517d": { "model_module": "@jupyter-widgets/controls", "model_module_version": "1.5.0", "model_name": "FloatProgressModel", "state": { "_dom_classes": [], "_model_module": "@jupyter-widgets/controls", "_model_module_version": "1.5.0", "_model_name": "FloatProgressModel", "_view_count": null, "_view_module": "@jupyter-widgets/controls", "_view_module_version": "1.5.0", "_view_name": "ProgressView", "bar_style": "success", "description": "", "description_tooltip": null, "layout": 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