Intro.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "yDU925Nhtz-j",
    "outputId": "835ebe5b-1fe8-4729-a8ee-93c7e5895e14"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
      "Requirement already satisfied: datasets in /usr/local/lib/python3.7/dist-packages (2.4.0)\n",
      "Requirement already satisfied: einops in /usr/local/lib/python3.7/dist-packages (0.4.1)\n",
      "Requirement already satisfied: huggingface-hub<1.0.0,>=0.1.0 in /usr/local/lib/python3.7/dist-packages (from datasets) (0.8.1)\n",
      "Requirement already satisfied: fsspec[http]>=2021.11.1 in /usr/local/lib/python3.7/dist-packages (from datasets) (2022.5.0)\n",
      "Requirement already satisfied: tqdm>=4.62.1 in /usr/local/lib/python3.7/dist-packages (from datasets) (4.64.0)\n",
      "Requirement already satisfied: aiohttp in /usr/local/lib/python3.7/dist-packages (from datasets) (3.8.1)\n",
      "Requirement already satisfied: xxhash in /usr/local/lib/python3.7/dist-packages (from datasets) (3.0.0)\n",
      "Requirement already satisfied: responses<0.19 in /usr/local/lib/python3.7/dist-packages (from datasets) (0.18.0)\n",
      "Requirement already satisfied: importlib-metadata in /usr/local/lib/python3.7/dist-packages (from datasets) (4.12.0)\n",
      "Requirement already satisfied: pandas in /usr/local/lib/python3.7/dist-packages (from datasets) (1.3.5)\n",
      "Requirement already satisfied: pyarrow>=6.0.0 in /usr/local/lib/python3.7/dist-packages (from datasets) (6.0.1)\n",
      "Requirement already satisfied: requests>=2.19.0 in /usr/local/lib/python3.7/dist-packages (from datasets) (2.23.0)\n",
      "Requirement already satisfied: numpy>=1.17 in /usr/local/lib/python3.7/dist-packages (from datasets) (1.21.6)\n",
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      "Requirement already satisfied: aiosignal>=1.1.2 in /usr/local/lib/python3.7/dist-packages (from aiohttp->datasets) (1.2.0)\n",
      "Requirement already satisfied: asynctest==0.13.0 in /usr/local/lib/python3.7/dist-packages (from aiohttp->datasets) (0.13.0)\n",
      "Requirement already satisfied: frozenlist>=1.1.1 in /usr/local/lib/python3.7/dist-packages (from aiohttp->datasets) (1.3.0)\n",
      "Requirement already satisfied: attrs>=17.3.0 in /usr/local/lib/python3.7/dist-packages (from aiohttp->datasets) (21.4.0)\n",
      "Requirement already satisfied: charset-normalizer<3.0,>=2.0 in /usr/local/lib/python3.7/dist-packages (from aiohttp->datasets) (2.1.0)\n",
      "Requirement already satisfied: multidict<7.0,>=4.5 in /usr/local/lib/python3.7/dist-packages (from aiohttp->datasets) (6.0.2)\n",
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      "Requirement already satisfied: yarl<2.0,>=1.0 in /usr/local/lib/python3.7/dist-packages (from aiohttp->datasets) (1.7.2)\n",
      "Requirement already satisfied: zipp>=0.5 in /usr/local/lib/python3.7/dist-packages (from importlib-metadata->datasets) (3.8.1)\n",
      "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/local/lib/python3.7/dist-packages (from pandas->datasets) (2.8.2)\n",
      "Requirement already satisfied: pytz>=2017.3 in /usr/local/lib/python3.7/dist-packages (from pandas->datasets) (2022.1)\n",
      "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.7/dist-packages (from python-dateutil>=2.7.3->pandas->datasets) (1.15.0)\n"
     ]
    }
   ],
   "source": [
    "%pip install datasets einops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 342,
     "referenced_widgets": [
      "f6dee54ac8c8435bad8c3f638facb750",
      "0dc8e209f4774dc39a9cefd016fc623b",
      "2e9592b2895b48e992a4e1b13d100970",
      "b05bb0c4a86d458b99505369dc848c95",
      "f57c6009b2a04c5c953e3cf09275dec5",
      "8597cfc32655417094f5eb5b79694df9",
      "7a684d614eff4d71843a006f97789354",
      "ecda664620bb4b1d89b1f132d9fa7e4f",
      "f6a7b7cbaf78471db5f3f7be87479ce3",
      "4b94ac5471e2461999c3503c5ec6874d",
      "8f3f879507794561a9772ab09a83a3a6"
     ]
    },
    "id": "c5QQMclRt7c7",
    "outputId": "4f80a44d-7c9b-471c-d61c-6c4df68bc6a9"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:datasets.builder:Reusing dataset cifar10 (/root/.cache/huggingface/datasets/cifar10/plain_text/1.0.0/447d6ec4733dddd1ce3bb577c7166b986eaa4c538dcd9e805ba61f35674a9de4)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f6dee54ac8c8435bad8c3f638facb750",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/2 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=640x256 at 0x7F26335C0950>"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load 10 images\n",
    "from PIL import Image\n",
    "from datasets import load_dataset\n",
    "\n",
    "cifar10 = load_dataset(\"cifar10\")\n",
    "W = H = 32\n",
    "cols, rows = 5, 2\n",
    "img = Image.new(\"RGB\", size=(W * cols, H * rows))\n",
    "for i in range(10):\n",
    "    # ignore label\n",
    "    im = cifar10[\"train\"][i][\"img\"]\n",
    "    left, top = W * (i % cols), H * (i // cols)\n",
    "    img.paste(im, (left, top))\n",
    "img.resize((W * cols * 4, H * rows * 4), Image.NEAREST)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "GfED0N0hsWk2"
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "import math\n",
    "\n",
    "\n",
    "def lin_schedule(start, end, T):\n",
    "    beta = torch.linspace(start, end, steps=T)\n",
    "    alpha = 1 - beta\n",
    "    alpha_bar = torch.cumprod(alpha, dim=0)\n",
    "    return alpha_bar\n",
    "\n",
    "\n",
    "# > In particular, we\n",
    "# > selected s such that \\sqrt{B_0}\n",
    "# > was slightly smaller than the pixel\n",
    "# > bin size 1/127.5, which gives  s = 0.008\n",
    "def cos_schedule(T, s=0.008):\n",
    "    alpha_bar = torch.arange(0, T)\n",
    "    assert alpha_bar.shape == (T,)\n",
    "\n",
    "    alpha_bar = ((alpha_bar / T) + s) / (1 + s)\n",
    "    alpha_bar *= math.pi / 2\n",
    "    alpha_bar = alpha_bar.cos() ** 2\n",
    "    return alpha_bar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "80glU7K-ybKi"
   },
   "outputs": [],
   "source": [
    "# > We set T = 1000 without a sweep, and we chose a linear\n",
    "# > schedule from β_1 = 10−4  to β_T = 0.02. [0]\n",
    "T = 1000\n",
    "lin_start = 1e-4\n",
    "lin_end = 0.02\n",
    "\n",
    "# Alternate parameters for experimentation\n",
    "# The cosine schedule always starts at 1 and ends at 0\n",
    "# with a smooth linear slope in the middle\n",
    "# Since `alpha_bar` is a cumulative product in the linear schedule\n",
    "# If we decrease the # of steps, we need to increase `lin_end` proportionally\n",
    "# to end @ 0\n",
    "# T = 100\n",
    "# Increasing this parameter steepens the slope\n",
    "# lin_start = 1e-4\n",
    "# lin_end = 0.2\n",
    "\n",
    "# Note: Modifying T should not change the curve for the cosine schedule,\n",
    "# (& if you tweak the linear schedule parameters, that curve won't change either)\n",
    "# so the sample image will be degraded at the same rate\n",
    "\n",
    "lin_alpha_bars = lin_schedule(start=lin_start, end=lin_end, T=T)\n",
    "cos_alpha_bars = cos_schedule(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 279
    },
    "id": "tB6uwES937uo",
    "outputId": "374accc6-7d70-4a13-9590-d19abc7e624d"
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = torch.arange(0, T)\n",
    "\n",
    "plt.plot(x, lin_alpha_bars, label=\"linear\")\n",
    "plt.plot(x, cos_alpha_bars, label=\"cosine\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FRiO9OtS5gci"
   },
   "source": [
    "Because the cosine schedule decreases $\\bar{a}$ more slowly, the co-efficient of the $\\epsilon$ term increases more slowly.\n",
    "\n",
    "Thus, noise is injected into the image more slowly.\n",
    "\n",
    "$q(x_t|x_0) = \\mathbb{N}(x_t;\\sqrt{\\bar{a}_t}x_0,(1-\\bar{a}_t)\\mathbb{I})$\n",
    "\n",
    "$x_t = \\sqrt{\\bar{a}_t}x_0 + \\sqrt{1 - \\bar{a}_t}\\epsilon$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "TWmeKpE55eSM"
   },
   "outputs": [],
   "source": [
    "from einops import rearrange\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "def q_xt_x0(t, x_0, abar):\n",
    "    scaled = x_0 * abar[t].sqrt()\n",
    "    # eps ~ N(0, I) [1]\n",
    "    eps = torch.randn_like(x_0)\n",
    "    noise = (1 - abar[t]).sqrt() * eps\n",
    "    return scaled + noise\n",
    "\n",
    "\n",
    "def img_to_tensor(img):\n",
    "    scaled_0_to_1 = np.array(im.convert(\"RGB\")) / 255\n",
    "    channels_first = rearrange(scaled_0_to_1, \"h w c -> c h w\")\n",
    "    neg_one_to_pos_one = channels_first * 2 - 1\n",
    "    return torch.tensor(neg_one_to_pos_one)\n",
    "\n",
    "\n",
    "def tensor_to_image(t):\n",
    "    channels_last = rearrange(t, \"c h w -> h w c\")\n",
    "    zero_to_255 = ((channels_last + 1) / 2).clip(0, 1) * 255\n",
    "    return Image.fromarray(np.array(zero_to_255).astype(np.uint8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 180
    },
    "id": "8KvLYFbc5eNn",
    "outputId": "9deedfb0-f364-42a9-8f18-801ca39179b5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Image dimensions: 32x32\n",
      "Tensor shape: torch.Size([3, 32, 32])\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=640x128 at 0x7F26A88A6490>"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_img = cifar10[\"train\"][0][\"img\"]\n",
    "# sample_img = sample_img.resize((64, 64), Image.NEAREST)\n",
    "print(f\"Image dimensions: {sample_img.height}x{sample_img.width}\")\n",
    "sample_img = img_to_tensor(sample_img)\n",
    "print(f\"Tensor shape: {sample_img.shape}\")\n",
    "samples = 10\n",
    "\n",
    "\n",
    "def q_samples(img, abar, samples, T):\n",
    "    idxs = torch.linspace(0, T - 1, steps=samples).int()\n",
    "    ims = []\n",
    "    for idx in idxs:\n",
    "        im = q_xt_x0(idx, img, abar)\n",
    "        ims.append(im)\n",
    "    return ims\n",
    "\n",
    "\n",
    "def compare_schedules(img, samples, T, abars):\n",
    "    all_samples = []\n",
    "    for abar in abars:\n",
    "        all_samples.append(q_samples(img, abar, samples, T))\n",
    "\n",
    "    _, W, H = img.shape\n",
    "    image = Image.new(\"RGB\", size=(W * samples, H * len(abars)))\n",
    "    for row, schedule_samples in enumerate(all_samples):\n",
    "        for col, sample in enumerate(schedule_samples):\n",
    "            sample = tensor_to_image(sample)\n",
    "            image.paste(sample, (W * col, H * row))\n",
    "    return image\n",
    "\n",
    "\n",
    "comparison = compare_schedules(sample_img, samples, T, [lin_alpha_bars, cos_alpha_bars])\n",
    "W, H = comparison.width, comparison.height\n",
    "# TODO: This looks a bit suspicious. Specifically,\n",
    "# it seems the car is getting destroyed a bit too quickly in both schedules\n",
    "# BUT, this might just be because the car image is low resolution\n",
    "comparison.resize((W * 2, H * 2), Image.NEAREST)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "f0TGnaBa7Fj7"
   },
   "source": [
    "$$\n",
    "p_\\theta(x_{t-1}|x_t) := \\mathcal{N}(x_{t-1};\\mu_\\theta(x_t,t),\\Sigma_\\theta(x_t,t))\n",
    "$$\n",
    "\n",
    "The original paper didn't learn the variance. It just fixed it to $\\sigma^2_t\\bf{I}$ where $\\sigma^2_t$ could either be \n",
    "- $\\beta_t$ (the upper bound)\n",
    "- $\\tilde{\\beta_t}$ (the lower bound)\n",
    "\n",
    "where $\\tilde{\\beta_t}$ represents the accumulated variance.\n",
    "\n",
    "$$\n",
    "\\tilde{\\beta_t} = \\frac{1-\\bar{a}_{t-1}}{1-\\bar{a}_t} \\cdot \\beta_t\n",
    "$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\n",
    "\\beta_t = 1 - \\frac{\\bar{a}_t}{\\bar{a}_{t-1}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 484
    },
    "id": "goxb6ayoSOmz",
    "outputId": "4cc625ae-f74f-444a-87e5-fbb20e2c2c2f"
   },
   "outputs": [
    {
     "ename": "AssertionError",
     "evalue": "ignored",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-185-848c16b67038>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     67\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mopenai_cos_alpha_bar\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mmy_cos_alpha_bar\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     68\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 69\u001b[0;31m   \u001b[0mtesting\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0massert_close\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mopenai_cos_alpha_bar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmy_cos_alpha_bar\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     70\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     71\u001b[0m   \u001b[0mopenai_betas\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbetas_for_alpha_bar\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcos_alpha_bar\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/torch/testing/_comparison.py\u001b[0m in \u001b[0;36massert_close\u001b[0;34m(actual, expected, allow_subclasses, rtol, atol, equal_nan, check_device, check_dtype, check_layout, check_stride, msg)\u001b[0m\n\u001b[1;32m   1359\u001b[0m         \u001b[0mcheck_layout\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcheck_layout\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1360\u001b[0m         \u001b[0mcheck_stride\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcheck_stride\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1361\u001b[0;31m         \u001b[0mmsg\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmsg\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   1362\u001b[0m     )\n",
      "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/torch/testing/_comparison.py\u001b[0m in \u001b[0;36massert_equal\u001b[0;34m(actual, expected, pair_types, sequence_types, mapping_types, msg, **options)\u001b[0m\n\u001b[1;32m   1093\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1094\u001b[0m     \u001b[0;31m# TODO: compose all metas into one AssertionError\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1095\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0merror_metas\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mto_error\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\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   1096\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1097\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAssertionError\u001b[0m: Scalars are not close!\n\nAbsolute difference: 1.5173078626862235e-07 (up to 1e-07 allowed)\nRelative difference: 3.5790783258528593e-07 (up to 1e-07 allowed)\n\nThe failure occurred for item [545]"
     ]
    }
   ],
   "source": [
    "from torch import testing\n",
    "\n",
    "# Testing my implementation of alpha_bar vs OpenAI's\n",
    "\n",
    "# OpenAI code\n",
    "def cos_alpha_bar(t):\n",
    "    return math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2\n",
    "\n",
    "\n",
    "def betas_for_alpha_bar(num_diffusion_timesteps, alpha_bar, max_beta=0.999):\n",
    "    \"\"\"\n",
    "    Create a beta schedule that discretizes the given alpha_t_bar function,\n",
    "    which defines the cumulative product of (1-beta) over time from t = [0,1].\n",
    "\n",
    "    :param num_diffusion_timesteps: the number of betas to produce.\n",
    "    :param alpha_bar: a lambda that takes an argument t from 0 to 1 and\n",
    "                      produces the cumulative product of (1-beta) up to that\n",
    "                      part of the diffusion process.\n",
    "    :param max_beta: the maximum beta to use; use values lower than 1 to\n",
    "                     prevent singularities.\n",
    "    \"\"\"\n",
    "    betas = []\n",
    "    for i in range(num_diffusion_timesteps):\n",
    "        t1 = i / num_diffusion_timesteps\n",
    "        t2 = (i + 1) / num_diffusion_timesteps\n",
    "        betas.append(min(1 - alpha_bar(t2) / alpha_bar(t1), max_beta))\n",
    "    return np.array(betas)\n",
    "\n",
    "\n",
    "# My code\n",
    "def cos_schedule_inclusive(T, s=0.008):\n",
    "    alpha_bar = torch.arange(0, T + 1)\n",
    "    assert alpha_bar.shape == (T + 1,)\n",
    "\n",
    "    alpha_bar = ((alpha_bar / T) + s) / (1 + s)\n",
    "    alpha_bar *= math.pi / 2\n",
    "    alpha_bar = alpha_bar.cos() ** 2\n",
    "    return alpha_bar\n",
    "\n",
    "\n",
    "def beta_and_agg_beta(alpha_bar, max_beta=0.999):\n",
    "    betas = []\n",
    "    for i in range(len(alpha_bar) - 1):\n",
    "        a_next = alpha_bar[i + 1]\n",
    "        a = alpha_bar[i]\n",
    "        betas.append(min(1 - a_next / a, max_beta))\n",
    "    return np.array(betas)\n",
    "\n",
    "    # From the cos vs lin alpha_bar plot we see alpha_bar starts @ 1 and heads to 0\n",
    "    alphas_bar_prev = alpha_bar.numpy()  # np.append(1.0, alpha_bar[:-1])\n",
    "    alphas_bar_next = np.append(alpha_bar[1:], 0.0)\n",
    "\n",
    "    beta = 1 - (alphas_bar_next / alphas_bar_prev)\n",
    "    beta = beta.clip(max=max_beta)\n",
    "    agg_beta = beta * ((1 - alphas_bar_prev) / (1 - alphas_bar_next))\n",
    "    return beta, agg_beta\n",
    "\n",
    "\n",
    "# Testing code\n",
    "for T in [100, 1000]:\n",
    "    # Tweaking s from 0.008 causes testing to throw an error (which is good)\n",
    "    my_cos_alpha_bar = cos_schedule_inclusive(T, s=0.008).tolist()\n",
    "    openai_cos_alpha_bar = [cos_alpha_bar(i / T) for i in range(T + 1)]\n",
    "\n",
    "    my_cos_alpha_bar = cos_schedule(T, s=0.008).tolist()\n",
    "    openai_cos_alpha_bar = [cos_alpha_bar(i / T) for i in range(T)]\n",
    "\n",
    "    manual_test = False\n",
    "    if manual_test:\n",
    "        i = 10\n",
    "        print(openai_cos_alpha_bar[i] - my_cos_alpha_bar[i])\n",
    "\n",
    "    testing.assert_close(openai_cos_alpha_bar, my_cos_alpha_bar)\n",
    "\n",
    "    openai_betas = betas_for_alpha_bar(T, cos_alpha_bar)\n",
    "\n",
    "    def from_list(l, x):\n",
    "        idx = x * T\n",
    "        return l[int(idx)]\n",
    "\n",
    "    # my_betas = betas_for_alpha_bar(T, lambda x: from_list(openai_cos_alpha_bar, x))\n",
    "    # my_betas = beta_and_agg_beta(my_cos_alpha_bar)\n",
    "    # assert len(my_betas) == len(openai_betas)\n",
    "    # print(openai_betas[2] - my_betas[3])\n",
    "    # testing.assert_close(openai_betas, my_betas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 574
    },
    "id": "fI_rZx4XADJb",
    "outputId": "44393114-1640-44da-fe87-bae6f705e8e6"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.         0.08168025 0.22458027 0.34069681 0.4299188  0.49920703\n",
      " 0.55414538 0.59861887 0.63529592 0.66603655 0.69216513 0.71464547\n",
      " 0.73419357 0.75135137 0.76653608 0.78007382 0.79222303 0.80319102\n",
      " 0.81314602 0.82222589 0.83054467 0.83819748 0.84526431 0.85181288\n",
      " 0.85790089 0.86357785 0.86888643 0.87386364 0.87854171 0.88294886\n",
      " 0.88710988 0.89104666 0.89477859 0.89832291 0.901695   0.90490861\n",
      " 0.90797612 0.91090863 0.91371619 0.9164079  0.918992   0.92147598\n",
      " 0.9238667  0.9261704  0.9283928  0.93053915 0.93261427 0.93462262\n",
      " 0.93656827 0.93845504 0.94028642 0.94206566 0.94379579 0.94547962\n",
      " 0.94711976 0.94871866 0.95027861 0.95180173 0.95329003 0.95474539\n",
      " 0.95616956 0.95756422 0.95893093 0.96027116 0.9615863  0.96287768\n",
      " 0.96414654 0.96539406 0.96662137 0.96782954 0.96901959 0.97019248\n",
      " 0.97134914 0.97249045 0.97361727 0.9747304  0.97583061 0.97691867\n",
      " 0.97799528 0.97906115 0.98011694 0.9811633  0.98220085 0.98323021\n",
      " 0.98425197 0.9852667  0.98627495 0.98727728 0.98827422 0.9892663\n",
      " 0.99025403 0.9912379  0.99221843 0.9931961  0.99417139 0.99514479\n",
      " 0.99611678 0.99708782 0.99805839 0.99902896]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def cos_alpha_bar(t):\n",
    "  return math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2\n",
    "\n",
    "def cos_betas(T):\n",
    "        return betas_for_alpha_bar(\n",
    "            T,\n",
    "            cos_alpha_bar\n",
    "        )\n",
    "\n",
    "\n",
    "def betas_for_alpha_bar(num_diffusion_timesteps, alpha_bar, max_beta=0.999):\n",
    "    \"\"\"\n",
    "    Create a beta schedule that discretizes the given alpha_t_bar function,\n",
    "    which defines the cumulative product of (1-beta) over time from t = [0,1].\n",
    "\n",
    "    :param num_diffusion_timesteps: the number of betas to produce.\n",
    "    :param alpha_bar: a lambda that takes an argument t from 0 to 1 and\n",
    "                      produces the cumulative product of (1-beta) up to that\n",
    "                      part of the diffusion process.\n",
    "    :param max_beta: the maximum beta to use; use values lower than 1 to\n",
    "                     prevent singularities.\n",
    "    \"\"\"\n",
    "    betas = []\n",
    "    for i in range(num_diffusion_timesteps):\n",
    "        t1 = i / num_diffusion_timesteps\n",
    "        t2 = (i + 1) / num_diffusion_timesteps\n",
    "        betas.append(min(1 - alpha_bar(t2) / alpha_bar(t1), max_beta))\n",
    "    return np.array(betas)\n",
    "\n",
    "def agg_betas(beta):\n",
    "  alpha = 1 - beta\n",
    "  alpha_bar = alpha.cumprod(axis=0)\n",
    "  alpha_bar_prev = np.append(1.0, alpha_bar[:-1])\n",
    "  alpha_bar_next = np.append(alpha_bar[1:], 0.0)\n",
    "  agg_beta = beta * ((1 - alpha_bar_prev) / (1 - alpha_bar_next))\n",
    "  return agg_beta \n",
    "\n",
    "\n",
    "# Plot B_t, agg_B_t, and their ratio\n",
    "# agg_B_t = \\tilde{\\beta_t}\n",
    "\n",
    "# For some reason, this method\n",
    "def beta_and_agg_beta(alpha_bar):\n",
    "  # From the cos vs lin alpha_bar plot we see alpha_bar starts @ 1 and heads to 0\n",
    "  alphas_bar_prev = np.append(1.0, alpha_bar[:-1])\n",
    "  alphas_bar_next = np.append(alpha_bar[1:], 0.0)\n",
    "\n",
    "  beta = 1 - (alphas_bar_next / alphas_bar_prev)\n",
    "  agg_beta = beta * ((1 - alphas_bar_prev) / (1 - alphas_bar_next))\n",
    "  # print(beta - agg_beta)\n",
    "  return beta, agg_beta\n",
    "\n",
    "T = 100\n",
    "cos_alpha_bars = cos_schedule(T)\n",
    "cos_alpha_bars = [cos_alpha_bar(i / T) for i in range(T)]\n",
    "for i, x in enumeratecos_alpha_bars:\n",
    "\n",
    "beta = cos_betas(T)\n",
    "agg_beta = agg_betas(beta)\n",
    "beta, agg_beta = beta_and_agg_beta(cos_alpha_bars)\n",
    "#cos_alpha_bars = cos_schedule(T)\n",
    "# beta, agg_beta = beta_and_agg_beta(cos_alpha_bars)\n",
    "# beta = betas2(T)\n",
    "# print(beta - agg_beta)\n",
    "ratio = agg_beta / beta\n",
    "print(ratio[:100])\n",
    "\n",
    "x = torch.arange(0, T)\n",
    "plt.xlabel(\"t\")\n",
    "plt.plot(x, beta, label=\"beta\")\n",
    "plt.plot(x, agg_beta, label=\"agg_beta\")\n",
    "plt.plot(x, ratio, label=\"agg_beta/beta\")\n",
    "plt.legend()\n",
    "plt.show()"
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