{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "86816b6d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "01b07a3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(3.0000)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.exp(torch.tensor(1.0986))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4f29d965",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = torch.linspace(0,1,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1b115c12",
   "metadata": {},
   "outputs": [],
   "source": [
    "t_i = (3*t) / (2*t + 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3c32dc7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(2.4596)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.exp(torch.tensor(0.9))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "aec3ae8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7ea4980d6b30>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qwenimage.sampling import TimestepDistUtils\n",
    "\n",
    "t = torch.linspace(0,1,100)\n",
    "t_i = TimestepDistUtils.t_shift(\n",
    "    mu=torch.tensor(2.0),\n",
    "    sigma=1.0,\n",
    "    t=t\n",
    ")\n",
    "plt.plot(t, t_i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3bc68e7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0986122886681098"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "math.log(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "facb782e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1.0000, 0.8808, 0.0000])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = torch.tensor([1, 0.5, 0])\n",
    "t_i = TimestepDistUtils.t_shift(\n",
    "    mu=torch.tensor(2.0),\n",
    "    sigma=1.0,\n",
    "    t=t\n",
    ")\n",
    "t_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f006f2fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1.0000, 0.7484, 0.0000])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = torch.tensor([1, 0.5, 0])\n",
    "t_i = TimestepDistUtils.t_shift(\n",
    "    mu=torch.tensor(1.09),\n",
    "    sigma=1.0,\n",
    "    t=t\n",
    ")\n",
    "t_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "779db3b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 6779.,  7062.,  7272.,  7391.,  7546.,  7954.,  8025.,  8172.,\n",
       "         8474.,  8836.,  9062.,  9219.,  9628.,  9980., 10461., 10679.,\n",
       "        11036., 11259., 11641., 12301., 12833., 13104., 13712., 14194.,\n",
       "        14489., 15417., 16018., 16705., 17465., 18281., 18923., 19943.,\n",
       "        20870., 21771., 22963., 23852., 24994., 26962., 28253., 29598.,\n",
       "        31810., 33453., 35445., 37914., 39958., 43009., 45798., 49379.,\n",
       "        52982., 57128.]),\n",
       " array([1.5955233e-06, 2.0001560e-02, 4.0001523e-02, 6.0001489e-02,\n",
       "        8.0001451e-02, 1.0000142e-01, 1.2000138e-01, 1.4000134e-01,\n",
       "        1.6000131e-01, 1.8000127e-01, 2.0000124e-01, 2.2000121e-01,\n",
       "        2.4000117e-01, 2.6000112e-01, 2.8000110e-01, 3.0000106e-01,\n",
       "        3.2000104e-01, 3.4000099e-01, 3.6000097e-01, 3.8000092e-01,\n",
       "        4.0000090e-01, 4.2000085e-01, 4.4000080e-01, 4.6000078e-01,\n",
       "        4.8000073e-01, 5.0000072e-01, 5.2000070e-01, 5.4000062e-01,\n",
       "        5.6000060e-01, 5.8000058e-01, 6.0000056e-01, 6.2000048e-01,\n",
       "        6.4000046e-01, 6.6000044e-01, 6.8000036e-01, 7.0000035e-01,\n",
       "        7.2000033e-01, 7.4000031e-01, 7.6000023e-01, 7.8000021e-01,\n",
       "        8.0000019e-01, 8.2000011e-01, 8.4000009e-01, 8.6000007e-01,\n",
       "        8.8000005e-01, 8.9999998e-01, 9.1999996e-01, 9.3999994e-01,\n",
       "        9.5999992e-01, 9.7999984e-01, 9.9999982e-01], dtype=float32),\n",
       " <BarContainer object of 50 artists>)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample = torch.rand((1000000,))\n",
    "outputs = time_shift(\n",
    "    mu=torch.tensor(1.09),\n",
    "    sigma=1.0,\n",
    "    t=sample,\n",
    ")\n",
    "\n",
    "plt.hist(outputs.cpu().numpy(), bins=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f26905a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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r2VXEVdEWgYhIGLXO2UD8njlsjJ9MYXQHv+OERIVARCRcnGPYhqcpimrJuh63+50mZCoEIiJh0jl9Pp0yF5Hc806Ko1r6HSdkKgQiImHQoKyY4RueIrt5PJvirvM7TrWoEIiIhEGvHe/SMj+FlX3vwzWI8jtOtagQiIicrvxMBm15kbT2Y0iLOd/vNNWmQiAicrrm/heNSgtY2fdesBMOulwrqRCIiJyO/esh8VW2xF5Ldovaf/FYVVQIREROlXPw6f3Q5AySev3c7zSnTFcWi4icquT3YPs8uOKvHC5r7XeaU6YtAhGRU3EoGz5/EDoPgxF15+KxqmiLQESkGo6MKTR83Z/pk7efzwc/y4Flu31OdXq0RSAiUk1tstfTe8fbbI77ca2/10AoVAhERKrDlTFy7eMUNW7N6t53+50mLFQIRESq4axd79E+O4mVfe+lOKqV33HCQoVARCRUOWkM2/g0+9qOJKXzRL/ThI0KgYhIKJyDT35Ng7ISlgx8tE5eQXw8KgQiIqFIfg82fUpS77vIax7rd5qw8qwQmFmsmX1jZuvNbK2Z/bKKNmZmfzezLWaWZGbDvcojInLK8jPg099ClxFsjJ/sd5qw83KLoAT4jXOuHzAa+LmZ9a/U5jKgV/AxBXjRwzwiIqfm0/vhUA5cOQ1nDf1OE3aeFQLn3B7n3Irg81xgPdClUrNJwBsuYDHQ2sw6eZVJRKTaNn4KybNg7L3QsfK6bP1QI8cIzCweGAYsqTSpC7CrwutUji0WmNkUM0s0s8T09HTPcoqIHCU/Az76BXQYAOf92u80nvF8iAkzOwN4D7jHOZdTeXIVH3HHvOHcdGA6QEJCwjHTRUTC7e3FOzh/5T10Lsji86EvcHD5Xr8jecbTLQIziyJQBN5yzr1fRZNUoOLh965AmpeZRERC0X33h8Tu+5qk3ndzsGUfv+N4ysuzhgz4J7DeOff0cZp9BNwSPHtoNJDtnNvjVSYRkZBk7SBh3ZPsazOCDd1v8TuN57zcNTQGuBlYY2argu89CMQBOOdeAuYAlwNbgAKgbo/lKiJ1X1kpzJ4KwOLBT9TLs4Qq86wQOOe+pepjABXbOKDu3tZHROqf756Dnd+ROOhx8psdc+5KvaQri0VEjkhdDl//Cfr9kO1drvQ7TY1RIRARASg8CLNugxad4crn6tVYQiejQiAi4hx8dDfkpME1r0LTNn4nqlEqBCIiy16B9R/BhQ9D7Ei/09Q4FQIRiWx7kgI3oe95EZxTP+44Vl26eb2IRK5D2eS8OZlGjVrzadzvKVqW6nciX6gQiEhkKiuD2VM5ozCVf496haImbf1O5BvtGhKRyLTgr7BxDiv73kt62wS/0/hKWwQiEnk2fwnfPAGDfszGLjf5ncZ3IW0RmNlEM9PWg4jUfZlb4b3/hDMHwg+fjajrBY4n1C2C64Fnzew94DXn3HoPM4mIhN3bS3bSsKSAixdPplkpfNbnv8lfmeF3rFohpLV859xkAjeW2Qq8ZmaLgjeLaeFpOhGRcHFlnJv0O1rlbmXhkP8mv1lXvxPVGiHv7gneVOY94F2gE3AVsMLMIvPEWxGpU4ZufIbYfV+zot9v2Rtzrt9xapVQjxFcaWazga+BKGCUc+4yYAhwr4f5RERO3/LX6b/9NTbFXcembjf6nabWCfUYwTXA35xz8yu+6ZwrMLP/E/5YIiJhsn0+/O+v2dP+XJb3e0AHh6sQ6q6hPZWLgJn9GcA59++wpxIRCYeMLTDzZmjXk2+HPoVroDPmqxJqIbioivcuC2cQEZGwykuHt66BBo3gxpkUR+ncluM5YXk0szuBnwFnmVlShUktgIVeBhMROWVFuYEikLsXbv0Y2sQDO/1OVWudbDvpbeBT4L+AByq8n+ucO+BZKhGRU/Tuoq2MS/wZHQ+sYf7wv5OW1hHSVARO5GSFwDnnUszsmPsKm1lbFQMRqVXKyhid9BCdMhezaNDjpHUY63eiOiGULYKJwHLAcfTN6B3Qw6NcIiLV4xx8/iDxez5lZe972N51kt+J6owTFgLn3MTgz+41E0dE5BQteAqWvMiG+Mms76Gz2qsj1AvKxphZ8+DzyWb2tJnFeRtNRCRE302Drx+Hwdezou99ulagmkI9ffRFoMDMhgC/BXYAb3qWSkQkVEtfhi8eggFXwaTnQQMlV1uov7ES55wDJgHPOueeJXAKqYiIf1a8AXPuhT5XwNUvQ0NdMHYqQv2t5ZrZ74DJwFgza0hgzCEREV989/4LnJP0IHvaj2F+t8coS9zjd6Q6K9QtguuAIuA/nXN7gS7AX070ATN71cz2m1nycaaPN7NsM1sVfDxcreQiErlWz2R00kPsazuSBcOfoaxhY78T1WkhbREEF/5PV3i9E3jjJB+bAUw7SbsFR85MEhEJyfLX4eNfsr/dKOYN/zulDaP9TlTnhXrW0NVmtjm4Bp9jZrlmlnOizwQHqdMFZyISPktfho9/AT1/wLwR0yht1MzvRPVCqMcI/hv4oQe3qDzHzFYDacC9zrm1VTUysynAFIC4OJ21KhJJ3l4SGB6i7/bXGb7hKXZ1mMDCHk9qd1AYhXqMYJ8HRWAF0M05NwR4DvjgeA2dc9OdcwnOuYSYmJgwxxCRWs05Bmz5B8M3PMWOMy/m22F/VREIs1C3CBLNbCaBhXXRkTedc++f6hcHb3155PkcM3vBzNo753Q3aREJKCtjxPo/02fHW2zv/EMWD3pM9xTwQKi/0ZZAAXBxhfcccMqFwMzOJLCl4cxsFIGtk8xTnZ+I1DMlh+GDqfTZ8R4b4icHrxjWxWJeCPWsodurO2MzewcYD7Q3s1TgjwSvPXDOvUTg9pd3mlkJUAhcH7xoTUQiXVEuzJwM2+ayss+vWN/9dg0b4aGQCoGZ9SYwzERH59xAMxsMXOmce/x4n3HO3XCieTrnphE4vVREpPygcJOiTMYn/ow2uRtZMuhPbO/6I3+DRYBQt7NeBn4HFAM455KA670KJSKRqWXeNi5efDOt8rYxf/izKgI1JNRjBM2cc0vt6E2zEg/yiEiE6pixiPNX/obSBlH8e9QrZLYZ4nekiBFqIcgws7MIHCDGzK4BNLCHiIRH4mtMSPwNOc27M2/ENPKbdfE7UUQJtRD8HJgO9DWz3cB24CbPUolIZCgrhS8fhkXT2BtzHt8O+QslUWf4nSrinLAQmNmvK7ycA3xD4LhCPvAfVBh/SESkWg5lw/s/hU2fwqifMq/NVF0j4JOT/daP3HOgDzAS+JDAfYtvBuZ7mEtE6rP9G2DmTZCVApc/BaN+ggueNSQ172T3LH4UwMy+AIY753KDrx8B/uV5OhGpdxZ8+E9GJ/2ekobRfDvyZdJdAqgI+CrU7bA44HCF14eB+LCnEZH6q6wUvv4T56/8GxmtBrNg+NMURnf0O5UQeiF4E1hqZrMJnDl0FfC6Z6lEpH7Jz4D37oBt37A59lqW93tAA8fVIqEOMfGEmX0KnB9863bn3ErvYolIvbF9QaAIFGbBD//OspIJfieSSkI+RO+cW0Fg6GgRkZN6Z/F2Bm55iYFb/kFu8258O/otDpb08TuWVEHnaolI+OWkccHSO+h4IJFtXa4ksf9DlOhuYrWWCoGIhNfGz+DDn9GuqIBFgx5ne9dJfieSk1AhEJHwKMqFzx+EFW9Ax4F8NuIJcs7o4XcqCYEKgYicvh2LYPZP4eBOGHMPTHiQnOX7/E4lIVIhEJFT9u53Wxi05Xn6b3uN/KadWXT2DNJbDgcVgTpFhUBETk3aSi5ZNIU2uZvYEvsfrOh7HyWNmvudSk6BCoGIVM/hApj7X7BoGk0at2PuiGmkdRjndyo5DSoEIhK6bfPg419C1nYYfiv/23YKxVEt/U4lp0mFQERO6l/frmHYhqfpmfo+uc3iWDLqn+xvN8rvWBImKgQicnzOQdJMJs5/kCbFB1nX/XbW9PoZpQ2j/U4mYaRCICJV25sMc+6FnYvIbzWIuQkvkNWqv9+pxAMqBCJS7u0lO4kqzmXQ5hfovfMdDjdqwaqBj7Kt64/AGvgdTzyiQiAiAWVlxO/+mGEb/kr04QNsib2W1b1/weHGrfxOJh5TIRARSFkIXzzEuWkryWw1kHkJz3Og1QC/U0kNUSEQiWSZW+HLh2HDJ9CiM4sGP8H2zhO1GyjCeFYIzOxVYCKw3zk3sIrpBjwLXA4UALcF73kgIh6btSCJQVteotfOmZQ2iGJdr7vZ0P1mShs29Tua+MDLLYIZwDTgjeNMvwzoFXycDbwY/CkiXjmcD0v+wZXznqZRST5bY69mTa+fc6hJe7+TiY88KwTOuflmFn+CJpOAN5xzDlhsZq3NrJNzbo9XmUQiVvEhWP4aLPgr5KeTHjOWVX3uIbtFL7+TSS3g5zGCLsCuCq9Tg+8dUwjMbAowBSAuLq5GwonUC6XFsPL/wfy/QM5u6D4WJrzFvD2d/E4mtYifhcCqeM9V1dA5Nx2YDpCQkFBlGxGpoLQEkmeR+9mfaFGYSkbrwawe9Sj72p1dxaqWRDo/C0EqEFvhdVcgzacsIvVDSRGsehsWPgNZKRS36MvcEc+TFnM+WFXrXiL+FoKPgLvM7F0CB4mzdXxA5BQdzoflr8N3z0FuGnQeDpf8Xz47OECngspJeXn66DvAeKC9maUCfwSiAJxzLwFzCJw6uoXA6aO3e5VFpN46lA1LX+bQgmlEF2exr20Ca0f+kb3tzoFsq3oHrEglXp41dMNJpjvg5159v0i9dnAnLPlH4EbxRTkciDmP5LOmkNFmmN/JpA7SlcUidcjnn/8vfVPeIHbvlwDsPPNi1ne/TaOCymlRIRCp7cpKA0NALHqeS3Yt4XCjFmyIv4VN3W6goKlOA5XTp0IgUlsVHAhcA7DsFTi4A1p3I7HfA2zr+iPdJF7CSoVApDZxDlKXsf3TvxO393Malh1mf5vhbBh2D7s7TsBZQ78TSj2kQiBSGxTlwZr/gWWvwr41dG3YnK1dr2Jz3HUaBkI8p0Ig4hfnYM+qwO6f1TPhcC50HAQT/8bsonMpadTM74QSIVQIRGpafgYkzYSVb8H+tZQ2aMzOMy9mc9x1ZLQeAqWm/5lSo/TPTaQmlBbD5i9h1Vuw6TMoK4EuI1g64A/s6HQpxVEt/U4oEUyFQMQrzsGe1bDmXxQuf4emhzMpbNyWlG43sa3Lj8hu0dPvhCKACoFI+GVsgeRZsOZfkLkFGkSREXM+27r8iLSY83ANovxOKHIUFQKRcMhJg+T3yVz8Fu1y1uEw9rUdyY6Bf2RXx4s43LiV3wlFjkuFQORU5aTB+k9g3YewYyHgoNUAlve9j52dLqEwuqPfCUVCokIgUh0HtsP6j8hYNov2B5MAyG7egx0972RH58vIbR7vbz6RU6BCIHIizkH6Blj/Maz7CPatAaBBy36s6v0LUjteSM4ZPXwOKXJ6VAhEKisthp2LYNPngVM9M7cABrFnw8VPQL8f8tkmDfQv9YcKgQhAXjps+TKw8N/6NRTlUGpR7Gs3it39r2NXxws5FB0TaLvJ36gi4aZCIJGprCywm2fTF2Ss/Ih2B9dgOAqaxJAWcxG7O4xlX7vRGuZBIoIKgUSOnD2w7ZvAGv+2uZCfDoC1Gsianneyu8NYslr20z1+JeKoEEj9dTgfUhZ+v/BP3xB4v3kM9BgPPSZAzx/w+boiX2OK+E2FQOqPksOQtgJSFsC2ebBrCZQehoZNoNu5rGx7OXvan8PBFr0Da/2HARUBERUCqcNKimD38sBaf8oC2LUUSgoByGrRmz1xN7K3/TmktxlOacNon8OK1F4qBFJ3FB+C3YnfL/hTl0HJocC0joNgxK3QbQzvZXajqHEbf7OK1CEqBFJ75e0PrOXvWhL4mbYSSosAgzMHsaHrNexrO5L0NiO+H8snF2jsZ2iRukeFQGqHslLYv+77hf6uJZCVAkCpRXGg1QAy4q5nf5sE9rcdRnGUBnETCRcVAvFH7r7Agd3dKyB1KaQmwuE8AAqbtCe99VAy+l5DRushHGjZn7KGWs0X8YoKgXiv4EBgt07wkZ+yjOaH9gFQRgMOtuxDxpkTyWg9hPQ2Q8lv2gVMQziI1BRPC4GZXQo8CzQEXnHOPVlp+njgQ2B78K33nXOPeZlJPFaUG7grV9rKwNp+2krI2v799LZnkd5mBBtaDeBAq4EcaNmXUl29K+IrzwqBmTUEngcuAlKBZWb2kXNuXaWmC5xzE73KIR5xDnJ2w95k2LsG9iYFflZY6OdHdyKz1UAO9L4y8LNVf92bV6QW8nKLYBSwxTm3DcDM3gUmAZULgdR2pcWQvjGwoN+X/P1CvzCrvElusziyWvYhq9cVZLXsR2arARQ1aedjaBEJlZeFoAuwq8LrVODsKtqdY2argTTgXufc2soNzGwKMAUgLi7Og6gCBAZiy94J+9cHHukbAmfypG8MXKELlDRoQnaLXmS1v4CsFn3JatmHgy16U9Kouc/hReRUeVkIqjra5yq9XgF0c87lmdnlwAdAr2M+5Nx0YDpAQkJC5XlIdTkH2anBhf162L8h8DN9IxQXlDfLj+5I9hk9ORh3E1kt+5LVsi+5zeJwDXSOgUh94uX/6FQgtsLrrgTW+ss553IqPJ9jZi+YWXvnXIaHuSJHaTFk7YDMzZCxGTI2Bhf6G+FwbnmzgiYxZJ9xFtmdrya7xVlkn9GT7DN6aH++SITwshAsA3qZWXdgN3A9cGPFBmZ2JrDPOefMbBTQAMj0MFP941xgOOWMzYE7aWVuhozgz6wUKCspb1rYuG1gId9pYnBhH1jol1+VKyIRybNC4JwrMbO7gM8JnD76qnNurZlNDU5/CbgGuNPMSoBC4HrnnHb9VKXwYOCMnAPb4cDW7xf2GVugKLu8WWmDxuQ2iyOneXdy48eT0zyenObx5DaP1wJfRKrk6c5e59wcYE6l916q8HwaMM3LDHVGWRnk7Q0s6I8s8Cv+rHCGDgT23+c2jyen46WBhX7zbuQ0j6egaSecNfSpEyJSF+moX00qyoPsXXBw17EL+4M7vh9JEyizhuRHdyKvWVfy2v+AvGax5DaLLf+pi7BEJFxUCMLFucBa+8Gd3y/ss3eVvz6UsYPo4oNHfaSkYVNym3Ulr1ksebGjyW0aWNDnNYslv+mZuAZR/vRFRCKKCkGoSoshdy/kpAUW8Ect7IM/g4OmHVHSsCl5TTtT0LQT+WdeTH7TTuQ37Ux+087kNevKocbtNKaOiPhOhQCguDCwgC9/7IbcPZCTRuae7TQ7tI/ookys0mUQRVGtggv2TuR3GlFhQd+JgqadKYpqrQW9iNR6kVMIslNh6zfHLOjJ2X3MgViAw41aUBDdkaLojmS16EthdAcKojuWP/KbdtbVtCJSL0ROIdi3Fj66C4DCxu0oiO4YWLjHDKAg+szvX0d3pKBJBx2MFZGIETmFoNsYPhz3GYXRHSjTQVgRkXKRUwianEF+sy5+pxARqXUa+B1ARET8pUIgIhLhVAhERCKcCoGISIRTIRARiXAqBCIiEU6FQEQkwqkQiIhEOBUCEZEIp0IgIhLhVAhERCKcCoGISIRTIRARiXAqBCIiEU6FQEQkwqkQiIhEOBUCEZEIp0IgIhLhPC0EZnapmW00sy1m9kAV083M/h6cnmRmw73MIyIix/KsEJhZQ+B54DKgP3CDmfWv1OwyoFfwMQV40as8IiJSNS+3CEYBW5xz25xzh4F3gUmV2kwC3nABi4HWZtbJw0wiIlJJIw/n3QXYVeF1KnB2CG26AHsqNjKzKQS2GADyzGzjKWZqD2Sc4mfrKvU5MqjPEeCm0+tzt+NN8LIQWBXvuVNog3NuOjD9tAOZJTrnEk53PnWJ+hwZ1OfI4FWfvdw1lArEVnjdFUg7hTYiIuIhLwvBMqCXmXU3s8bA9cBHldp8BNwSPHtoNJDtnNtTeUYiIuIdz3YNOedKzOwu4HOgIfCqc26tmU0NTn8JmANcDmwBCoDbvcoTdNq7l+og9TkyqM+RwZM+m3PH7JIXEZEIoiuLRUQinAqBiEiEq5eFIBKHtgihzzcF+5pkZt+Z2RA/cobTyfpcod1IMys1s2tqMp8XQumzmY03s1VmttbM5tV0xnAL4d92KzP72MxWB/vs9bFGT5nZq2a238ySjzM9/Msv51y9ehA4ML0V6AE0BlYD/Su1uRz4lMB1DKOBJX7nroE+nwu0CT6/LBL6XKHd1wROTLjG79w18HduDawD4oKvO/iduwb6/CDw5+DzGOAA0Njv7KfR57HAcCD5ONPDvvyqj1sEkTi0xUn77Jz7zjmXFXy5mMA1G3VZKH9ngLuB94D9NRnOI6H0+UbgfefcTgDnXF3vdyh9dkALMzPgDAKFoKRmY4aPc24+gT4cT9iXX/WxEBxv2IrqtqlLqtuf/ySwRlGXnbTPZtYFuAp4qQZzeSmUv3NvoI2ZzTWz5WZ2S42l80YofZ4G9CNwMeoa4JfOubKaieeLsC+/vBxiwi9hG9qiDgm5P2Y2gUAhOM/TRN4Lpc/PAPc750oDK4t1Xih9bgSMAC4EmgKLzGyxc26T1+E8EkqfLwFWARcAZwFfmtkC51yOx9n8EvblV30sBJE4tEVI/TGzwcArwGXOucwayuaVUPqcALwbLALtgcvNrMQ590GNJAy/UP9tZzjn8oF8M5sPDAHqaiEIpc+3A0+6wA70LWa2HegLLK2ZiDUu7Muv+rhrKBKHtjhpn80sDngfuLkOrx1WdNI+O+e6O+finXPxwCzgZ3W4CEBo/7Y/BM43s0Zm1ozAiL/razhnOIXS550EtoAws45AH2BbjaasWWFfftW7LQJXO4e28FSIfX4YaAe8EFxDLnF1eOTGEPtcr4TSZ+fcejP7DEgCyoBXnHNVnoZYF4T4d/4TMMPM1hDYbXK/c67ODk9tZu8A44H2ZpYK/BGIAu+WXxpiQkQkwtXHXUMiIlINKgQiIhFOhUBEJMKpEIiIRDgVAhGRCKdCIHIazOw2M+t8Gp+PN7Mbw5lJpLpUCEROz23AKRcCIJ7AQHEivlEhEKnEzH5tZsnBxz3BtfbkCtPvNbNHgvc3SADeCo7/39TMUszsz2a2NPjoGfzMjIr3QzCzvODTJwlcCbzKzH5Vk/0UOUKFQKQCMxtB4ErNswmM9f4ToE1VbZ1zs4BE4Cbn3FDnXGFwUo5zbhSBUTGfOclXPgAsCH7+b2Hogki1qRCIHO08YLZzLt85l0dgfKbzqzmPdyr8PCec4US8oEIgcrSqhvhtzdH/V6JPMg9XxfOSI/MI3kCl8SnmEwk7FQKRo80HfmRmzcysOYEb23wKdDCzdmbWBJhYoX0u0KLSPK6r8HNR8HkKgfsEQOAOU1En+LxIjap3o4+KnA7n3Aozm8H3Y9m/4pxbZmaPAUuA7cCGCh+ZAbxkZoV8vxuoiZktIbCidUPwvZeBD81sKfBvID/4fhJQYmargRk6TiB+0OijImFkZilAQl0eBlkij3YNiYhEOG0RiIhEOG0RiIhEOBUCEZEIp0IgIhLhVAhERCKcCoGISIT7/3R1yWN0xilyAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "977b174e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "7f18226b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ 0.3832, -1.2497, -0.6377, -0.7938,  0.9490, -0.7611,  0.2699,  0.4623,\n",
       "         0.0484, -0.5507, -0.3517, -0.6463,  0.1703, -0.3150,  0.0628,  0.5831,\n",
       "        -1.0889, -1.0628,  0.4548, -0.1160, -0.0689,  0.2462, -0.1435, -0.3815,\n",
       "         0.7189, -0.0109, -0.0067, -0.8627,  0.2413,  1.0570, -0.2005, -1.0201,\n",
       "         1.1647, -1.2583, -0.3579,  0.1008, -0.3393, -0.9170, -0.6816,  1.1008,\n",
       "         0.0098,  0.9410,  0.4740, -0.0731,  0.4606,  0.2902,  0.1464,  0.6644,\n",
       "         1.9959,  0.6937,  0.4918, -2.0359, -1.5676, -0.7365,  0.2790,  2.0777,\n",
       "        -0.9764,  1.2429, -1.1259,  0.0556,  0.8841,  0.0918,  1.1493, -0.0938,\n",
       "         0.9685, -0.0640, -0.5289,  0.0269, -0.6180,  0.5492, -0.9579, -1.6734,\n",
       "        -0.5108,  1.9472,  0.1120,  0.9794,  0.3711,  1.6976, -0.8576, -0.6719,\n",
       "         0.2169, -0.8754, -0.5149,  0.6878,  0.0826, -0.0441, -1.2645,  1.1878,\n",
       "        -0.7726,  0.3082,  0.1578,  0.6367, -1.2092, -0.1273, -1.4948, -1.0086,\n",
       "         2.4209,  1.6574, -1.2036, -0.9799])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.randn((100,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "94b11b42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x713a770bce80>]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ls = torch.linspace(-2,2,100)\n",
    "\n",
    "plt.plot(ls, torch.logit(ls))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "d3a3c5fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor(nan), tensor(nan), tensor(nan))"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist_lg = torch.logit(torch.randn((100,)))\n",
    "\n",
    "dist_lg.min(), dist_lg.max(), dist_lg.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "b4bc9252",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x713a8a872e00>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qwenimage.sampling import get_lin_function\n",
    "\n",
    "mu_fn = get_lin_function(y1=0.5, y2=1.15)\n",
    "\n",
    "seq_lens = torch.linspace(0, 10000, 100)\n",
    "\n",
    "mus = mu_fn(seq_lens)\n",
    "\n",
    "\n",
    "plt.plot(mus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "580244b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x713a89645750>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, t_i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "b8c9b48a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x713a77640b80>]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = torch.linspace(0,1,100)\n",
    "\n",
    "u = torch.log(t / (1 - t))\n",
    "# sigmas = 1 / (1 + torch.exp(-u))\n",
    "\n",
    "plt.plot(t, u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "759e4db7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.00000e+00, 5.00000e+00, 1.00000e+00, 7.00000e+00, 8.00000e+00,\n",
       "        1.30000e+01, 1.90000e+01, 4.20000e+01, 7.50000e+01, 1.43000e+02,\n",
       "        2.02000e+02, 3.64000e+02, 6.50000e+02, 1.11400e+03, 2.07100e+03,\n",
       "        3.56500e+03, 5.99100e+03, 1.02520e+04, 1.75370e+04, 2.86130e+04,\n",
       "        4.56010e+04, 6.98140e+04, 9.73820e+04, 1.24446e+05, 1.37246e+05,\n",
       "        1.30413e+05, 1.07757e+05, 7.95450e+04, 5.33540e+04, 3.37370e+04,\n",
       "        2.08500e+04, 1.23450e+04, 7.09100e+03, 4.10500e+03, 2.43400e+03,\n",
       "        1.38400e+03, 7.62000e+02, 4.27000e+02, 2.64000e+02, 1.52000e+02,\n",
       "        9.40000e+01, 4.50000e+01, 3.70000e+01, 1.70000e+01, 6.00000e+00,\n",
       "        6.00000e+00, 5.00000e+00, 4.00000e+00, 0.00000e+00, 4.00000e+00]),\n",
       " array([-13.639799  , -13.087073  , -12.5343485 , -11.981623  ,\n",
       "        -11.428897  , -10.876172  , -10.323446  ,  -9.7707205 ,\n",
       "         -9.217996  ,  -8.66527   ,  -8.112544  ,  -7.5598187 ,\n",
       "         -7.0070934 ,  -6.454368  ,  -5.901643  ,  -5.348917  ,\n",
       "         -4.7961917 ,  -4.2434664 ,  -3.6907406 ,  -3.1380153 ,\n",
       "         -2.5852897 ,  -2.0325644 ,  -1.4798388 ,  -0.92711335,\n",
       "         -0.3743879 ,   0.17833757,   0.73106307,   1.2837886 ,\n",
       "          1.836514  ,   2.3892395 ,   2.9419649 ,   3.4946904 ,\n",
       "          4.0474157 ,   4.6001415 ,   5.152867  ,   5.705592  ,\n",
       "          6.258318  ,   6.8110433 ,   7.3637686 ,   7.916494  ,\n",
       "          8.469219  ,   9.021945  ,   9.574671  ,  10.127396  ,\n",
       "         10.680121  ,  11.232847  ,  11.785572  ,  12.338298  ,\n",
       "         12.891024  ,  13.443748  ,  13.996474  ], dtype=float32),\n",
       " <BarContainer object of 50 artists>)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# sample = torch.rand((1000000,))\n",
    "# outputs = time_shift(\n",
    "#     mu=torch.tensor(1.09),\n",
    "#     sigma=1.0,\n",
    "#     t=sample,\n",
    "# )\n",
    "\n",
    "\n",
    "\n",
    "sample = torch.rand((1000000,))\n",
    "\n",
    "outputs = torch.log(sample / (1 - sample))\n",
    "\n",
    "plt.hist(outputs.cpu().numpy(), bins=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c6b7ea01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([   -inf, -4.5850, -3.8816, -3.4657, -3.1676, -2.9339, -2.7408, -2.5759,\n",
       "        -2.4314, -2.3026, -2.1861, -2.0794, -1.9810, -1.8894, -1.8036, -1.7228,\n",
       "        -1.6463, -1.5735, -1.5041, -1.4376, -1.3737, -1.3122, -1.2528, -1.1952,\n",
       "        -1.1394, -1.0852, -1.0324, -0.9808, -0.9305, -0.8812, -0.8329, -0.7855,\n",
       "        -0.7390, -0.6931, -0.6480, -0.6035, -0.5596, -0.5162, -0.4733, -0.4308,\n",
       "        -0.3887, -0.3469, -0.3054, -0.2642, -0.2231, -0.1823, -0.1417, -0.1011,\n",
       "        -0.0606, -0.0202,  0.0202,  0.0606,  0.1011,  0.1417,  0.1823,  0.2231,\n",
       "         0.2642,  0.3054,  0.3469,  0.3887,  0.4308,  0.4733,  0.5162,  0.5596,\n",
       "         0.6035,  0.6480,  0.6931,  0.7390,  0.7855,  0.8329,  0.8812,  0.9305,\n",
       "         0.9808,  1.0324,  1.0852,  1.1394,  1.1952,  1.2528,  1.3122,  1.3737,\n",
       "         1.4376,  1.5041,  1.5735,  1.6463,  1.7228,  1.8036,  1.8894,  1.9810,\n",
       "         2.0794,  2.1861,  2.3026,  2.4314,  2.5759,  2.7408,  2.9339,  3.1676,\n",
       "         3.4657,  3.8816,  4.5850,     inf])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x713a776ab1f0>]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ls = torch.linspace(-2,2,100)\n",
    "\n",
    "plt.plot(ls, torch.logit(ls))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "\n",
    "def logit_normal_pdf(x, mu=0.0, sigma=1.0):\n",
    "\n",
    "    pdf = torch.zeros_like(x)\n",
    "    z = (torch.logit(x) - mu) / sigma\n",
    "    coef = 1.0 / (sigma * torch.sqrt(torch.tensor(2.0 * torch.pi)))\n",
    "    pdf = coef * torch.exp(-0.5 * z**2) / (x * (1.0 - x))\n",
    "\n",
    "    return pdf\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "1fb2d3ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7be630acf160>]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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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",
    "xs = torch.linspace(0, 1, 100)\n",
    "\n",
    "pdf_vals = logit_normal_pdf(xs, mu=0.0, sigma=1)\n",
    "plt.plot(xs, pdf_vals, 'b-o', label='PDF')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c147d838",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([       nan, 1.0867e-03, 1.0783e-02, 3.3463e-02, 6.8176e-02, 1.1246e-01,\n",
       "         1.6379e-01, 2.2003e-01, 2.7946e-01, 3.4072e-01, 4.0279e-01, 4.6488e-01,\n",
       "         5.2640e-01, 5.8690e-01, 6.4605e-01, 7.0361e-01, 7.5942e-01, 8.1335e-01,\n",
       "         8.6533e-01, 9.1531e-01, 9.6327e-01, 1.0092e+00, 1.0531e+00, 1.0950e+00,\n",
       "         1.1350e+00, 1.1730e+00, 1.2091e+00, 1.2433e+00, 1.2757e+00, 1.3064e+00,\n",
       "         1.3353e+00, 1.3625e+00, 1.3880e+00, 1.4119e+00, 1.4342e+00, 1.4549e+00,\n",
       "         1.4741e+00, 1.4918e+00, 1.5081e+00, 1.5229e+00, 1.5363e+00, 1.5483e+00,\n",
       "         1.5589e+00, 1.5681e+00, 1.5760e+00, 1.5825e+00, 1.5878e+00, 1.5917e+00,\n",
       "         1.5943e+00, 1.5956e+00, 1.5956e+00, 1.5943e+00, 1.5917e+00, 1.5878e+00,\n",
       "         1.5825e+00, 1.5760e+00, 1.5681e+00, 1.5589e+00, 1.5483e+00, 1.5363e+00,\n",
       "         1.5229e+00, 1.5081e+00, 1.4918e+00, 1.4741e+00, 1.4549e+00, 1.4342e+00,\n",
       "         1.4119e+00, 1.3880e+00, 1.3625e+00, 1.3353e+00, 1.3064e+00, 1.2757e+00,\n",
       "         1.2433e+00, 1.2091e+00, 1.1730e+00, 1.1350e+00, 1.0950e+00, 1.0531e+00,\n",
       "         1.0092e+00, 9.6327e-01, 9.1531e-01, 8.6533e-01, 8.1335e-01, 7.5942e-01,\n",
       "         7.0361e-01, 6.4605e-01, 5.8690e-01, 5.2640e-01, 4.6488e-01, 4.0279e-01,\n",
       "         3.4072e-01, 2.7946e-01, 2.2003e-01, 1.6379e-01, 1.1246e-01, 6.8176e-02,\n",
       "         3.3463e-02, 1.0783e-02, 1.0867e-03,        nan]),\n",
       " tensor([   nan, 0.0032, 0.0314, 0.0934, 0.1787, 0.2737, 0.3681, 0.4562, 0.5357,\n",
       "         0.6059, 0.6673, 0.7210, 0.7678, 0.8086, 0.8444, 0.8759, 0.9037, 0.9284,\n",
       "         0.9503, 0.9698, 0.9873, 1.0031, 1.0172, 1.0301, 1.0416, 1.0522, 1.0617,\n",
       "         1.0704, 1.0784, 1.0856, 1.0922, 1.0982, 1.1037, 1.1087, 1.1133, 1.1175,\n",
       "         1.1212, 1.1247, 1.1277, 1.1305, 1.1330, 1.1351, 1.1371, 1.1387, 1.1401,\n",
       "         1.1412, 1.1422, 1.1428, 1.1433, 1.1435, 1.1435, 1.1433, 1.1428, 1.1422,\n",
       "         1.1412, 1.1401, 1.1387, 1.1371, 1.1351, 1.1330, 1.1305, 1.1277, 1.1247,\n",
       "         1.1212, 1.1175, 1.1133, 1.1087, 1.1037, 1.0982, 1.0922, 1.0856, 1.0784,\n",
       "         1.0704, 1.0617, 1.0522, 1.0416, 1.0301, 1.0172, 1.0031, 0.9873, 0.9698,\n",
       "         0.9503, 0.9284, 0.9037, 0.8759, 0.8444, 0.8086, 0.7678, 0.7210, 0.6673,\n",
       "         0.6059, 0.5357, 0.4562, 0.3681, 0.2737, 0.1787, 0.0934, 0.0314, 0.0032,\n",
       "            nan]))"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pdf_vals, pdf_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "a59f2cd1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([3.0000e+01, 2.4500e+02, 7.0900e+02, 1.4760e+03, 2.2330e+03,\n",
       "        3.3000e+03, 4.4680e+03, 5.5020e+03, 6.9420e+03, 8.1690e+03,\n",
       "        9.4990e+03, 1.0613e+04, 1.2161e+04, 1.3611e+04, 1.4994e+04,\n",
       "        1.6161e+04, 1.7471e+04, 1.8815e+04, 2.0019e+04, 2.1471e+04,\n",
       "        2.2580e+04, 2.3668e+04, 2.5105e+04, 2.5886e+04, 2.7393e+04,\n",
       "        2.8233e+04, 2.9139e+04, 3.0581e+04, 3.1532e+04, 3.2268e+04,\n",
       "        3.3261e+04, 3.3459e+04, 3.4244e+04, 3.4954e+04, 3.4969e+04,\n",
       "        3.5175e+04, 3.5427e+04, 3.5251e+04, 3.4503e+04, 3.3396e+04,\n",
       "        3.2962e+04, 3.1003e+04, 2.9031e+04, 2.6470e+04, 2.3240e+04,\n",
       "        1.9258e+04, 1.4578e+04, 9.5810e+03, 4.2540e+03, 7.1000e+02]),\n",
       " array([0.01065848, 0.03034609, 0.0500337 , 0.06972132, 0.08940893,\n",
       "        0.10909654, 0.12878416, 0.14847177, 0.16815938, 0.187847  ,\n",
       "        0.20753461, 0.22722223, 0.24690984, 0.26659745, 0.28628507,\n",
       "        0.3059727 , 0.3256603 , 0.3453479 , 0.36503553, 0.38472313,\n",
       "        0.40441075, 0.42409837, 0.44378597, 0.4634736 , 0.4831612 ,\n",
       "        0.5028488 , 0.52253646, 0.54222405, 0.56191164, 0.5815993 ,\n",
       "        0.6012869 , 0.6209745 , 0.64066213, 0.6603497 , 0.6800373 ,\n",
       "        0.699725  , 0.71941257, 0.73910016, 0.7587878 , 0.7784754 ,\n",
       "        0.79816306, 0.81785065, 0.83753824, 0.8572259 , 0.8769135 ,\n",
       "        0.8966011 , 0.91628873, 0.9359763 , 0.9556639 , 0.9753516 ,\n",
       "        0.99503917], dtype=float32),\n",
       " <BarContainer object of 50 artists>)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ts = torch.sigmoid(torch.randn((1000000,)))\n",
    "\n",
    "\n",
    "ts_i = t_shift(\n",
    "    mu=torch.tensor(0.5),\n",
    "    sigma=1.0,\n",
    "    t=ts\n",
    ")\n",
    "plt.hist(ts_i.cpu().numpy(), bins=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e80a67ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "        0.4762, 0.6519, 0.2156, 0.7210, 0.4055, 0.7941, 0.4686, 0.3257, 0.6487,\n",
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       "        0.1394, 0.4971, 0.3274, 0.5662, 0.5707, 0.3110, 0.2316, 0.2840, 0.5235,\n",
       "        0.4130, 0.2476, 0.4011, 0.5161, 0.9290, 0.8998, 0.3940, 0.1164, 0.3647,\n",
       "        0.2644, 0.6955, 0.3877, 0.5106, 0.2276, 0.7781, 0.4690, 0.3693, 0.4249,\n",
       "        0.7080, 0.3488, 0.2810, 0.3888, 0.3258, 0.3143, 0.3025, 0.4297, 0.2667,\n",
       "        0.3196, 0.3723, 0.5656, 0.7129, 0.3242, 0.7305, 0.7307, 0.3819, 0.6992,\n",
       "        0.4292, 0.2189, 0.6281, 0.5879, 0.5768, 0.6776, 0.7140, 0.5749, 0.5088,\n",
       "        0.1635, 0.5169, 0.3170, 0.3619, 0.8209, 0.4363, 0.4964, 0.4621, 0.3399,\n",
       "        0.3914, 0.7791, 0.3636, 0.5856, 0.8219, 0.4989, 0.3631, 0.4615, 0.4004,\n",
       "        0.3413, 0.6819, 0.3943, 0.1865, 0.2577, 0.8251, 0.5649, 0.4675, 0.4724,\n",
       "        0.5645, 0.4928, 0.4292, 0.3970, 0.4055, 0.4876, 0.5581, 0.3741, 0.4741,\n",
       "        0.3573, 0.4205, 0.6891, 0.4500, 0.6595, 0.3405, 0.5043, 0.3335, 0.4914,\n",
       "        0.8487, 0.3686, 0.5925, 0.3705, 0.4259, 0.6256, 0.3108, 0.6790, 0.7163,\n",
       "        0.4510, 0.2481, 0.5012, 0.3100, 0.3960, 0.4258, 0.5645, 0.4050, 0.4496,\n",
       "        0.3670, 0.4677, 0.6142, 0.8826, 0.4698, 0.5746, 0.3413, 0.3843, 0.6665,\n",
       "        0.9068, 0.4904, 0.4912, 0.5345, 0.3207, 0.2550, 0.2148, 0.3086, 0.7188,\n",
       "        0.4624, 0.6450, 0.4571, 0.8294, 0.3734, 0.6607, 0.1784, 0.2809, 0.2761,\n",
       "        0.3128, 0.5247, 0.4912, 0.7421, 0.4419, 0.6583, 0.3835, 0.2148, 0.4234,\n",
       "        0.8134, 0.6209, 0.6653, 0.5330, 0.2983, 0.8073, 0.4064, 0.3496, 0.7615,\n",
       "        0.1899, 0.4105, 0.6044, 0.4615, 0.6718, 0.5946, 0.4136, 0.3009, 0.4031,\n",
       "        0.8802, 0.3113, 0.1832, 0.5272, 0.3064, 0.4817, 0.3445, 0.8322, 0.7766,\n",
       "        0.5150, 0.8568, 0.6240, 0.5702, 0.4278, 0.4786, 0.7214, 0.9421, 0.9007,\n",
       "        0.3219, 0.3764, 0.6224, 0.7009, 0.8369, 0.7728, 0.7847, 0.4996, 0.4370,\n",
       "        0.3988, 0.7001, 0.4897, 0.3883, 0.4942, 0.3107, 0.1315, 0.7197, 0.5222,\n",
       "        0.3697, 0.6138, 0.4794, 0.4163, 0.2790, 0.8135, 0.7243, 0.4567, 0.2627,\n",
       "        0.6431, 0.8032, 0.2577, 0.4489, 0.6172, 0.5094, 0.2175, 0.7788, 0.7776,\n",
       "        0.7462, 0.6744, 0.2767, 0.8898, 0.8257, 0.7282, 0.5920, 0.5540, 0.5634,\n",
       "        0.6816, 0.6322, 0.6582, 0.8019, 0.8368, 0.6744, 0.3273, 0.6141, 0.6923,\n",
       "        0.8059, 0.1967, 0.6420, 0.6973, 0.5236, 0.6245, 0.9448, 0.3691, 0.1866,\n",
       "        0.3422, 0.6528, 0.6087, 0.3695, 0.6736, 0.1359, 0.4725, 0.6163, 0.3558,\n",
       "        0.5825, 0.4280, 0.3647, 0.8750, 0.5009, 0.5483, 0.6290, 0.6025, 0.3471,\n",
       "        0.7580, 0.7527, 0.8512, 0.6091, 0.2758, 0.5398, 0.5493, 0.6839, 0.7161,\n",
       "        0.7817, 0.4392, 0.4344, 0.4952, 0.5157, 0.3370, 0.6558, 0.1334, 0.2998,\n",
       "        0.4568, 0.3986, 0.8062, 0.3166, 0.4290, 0.6904, 0.5222, 0.4808, 0.5651,\n",
       "        0.4730, 0.3950, 0.1606, 0.2678, 0.6917, 0.2595, 0.2742, 0.7051, 0.7833,\n",
       "        0.8293, 0.5924, 0.3514, 0.4440, 0.5675, 0.2300, 0.4893, 0.5912, 0.7702,\n",
       "        0.1734])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fc6e987b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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