SDXL latent space explorer

lviz.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "32011c59-8beb-4bd5-b655-7224ffb2aa00",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "from PIL import Image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "aec8d7c1-9b15-44f3-bf89-9649b55a9fe3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def latents_to_rgb(latents):\n",
    "    weights = (\n",
    "        (60, -60, 25, -70),\n",
    "        (60,  -5, 15, -50),\n",
    "        (60,  10, -5, -35)\n",
    "    )\n",
    "\n",
    "    weights_tensor = torch.t(torch.tensor(weights, dtype=latents.dtype).to(latents.device))\n",
    "    biases_tensor = torch.tensor((150, 140, 130), dtype=latents.dtype).to(latents.device)\n",
    "    rgb_tensor = torch.einsum(\"...lxy,lr -> ...rxy\", latents, weights_tensor) + biases_tensor.unsqueeze(-1).unsqueeze(-1)\n",
    "    image_array = rgb_tensor.clamp(0, 255)[0].byte().cpu().numpy()\n",
    "    image_array = image_array.transpose(1, 2, 0)  # Change the order of dimensions\n",
    "\n",
    "    return Image.fromarray(image_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "bd552a3c-7e0f-4445-91af-24c3478ba6ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": "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",
      "image/png": "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",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=128x128>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ones = torch.ones((1, 4, 128, 128), dtype=torch.float32)\n",
    "latents_to_rgb(ones)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "faa9713d-f868-450d-9e81-12fbb64bdd04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": "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",
      "image/png": "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",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=128x128>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "latents_to_rgb(ones * 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6bd1356b-fde1-4bd8-ba5e-bec256373420",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": "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",
      "image/png": "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",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=128x128>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "latents_to_rgb(ones * 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "6d93fade-68b2-4de8-bbc3-e3f430a985c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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",
      "image/png": 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",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=128x128>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ones_layer = torch.ones((1, 1, 128, 128), dtype=torch.float32)\n",
    "zero_layer = torch.zeros((1, 1, 128, 128), dtype=torch.float32)\n",
    "noise_layer = torch.randn((1, 1, 32, 32), dtype=torch.float32)\n",
    "\n",
    "pattern_noise = (torch.nn.functional.interpolate(noise_layer, scale_factor=4) - 0.5) * 2\n",
    "\n",
    "latents = torch.cat((zero_layer, ones_layer, ones_layer, pattern_noise), 1)\n",
    "latents_to_rgb(latents)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "ac087082-6ebe-4d9a-929a-f9cac98a365f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def pp(x):\n",
    "    pattern_noise = (torch.nn.functional.interpolate(noise_layer, scale_factor=4) - 0.5) * x\n",
    "\n",
    "    latents = torch.cat((zero_layer, ones_layer, ones_layer, pattern_noise), 1)\n",
    "    return latents_to_rgb(latents)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "1336ffe4-ec9d-4fc2-b202-887dd8dcb30a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": "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",
      "image/png": "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",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=128x128>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "f9614212-23f5-460d-ba14-8fc2b8d6815d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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",
      "image/png": "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",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=128x128>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "6f76aba7-7f02-49b6-9f2c-d962f049a554",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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",
      "image/png": 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",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=128x128>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "196220a0-3610-4e2f-8895-77a8c217c4e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ll(x):\n",
    "    pattern_noise = (torch.nn.functional.interpolate(noise_layer, scale_factor=4) - 0.5) * x\n",
    "\n",
    "    latents = torch.cat((pattern_noise, ones_layer, ones_layer, zero_layer), 1)\n",
    "    return latents_to_rgb(latents)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "d702a442-0c5c-492e-9a2a-409d4ab833d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": "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",
      "image/png": "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",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=128x128>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ll(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "657ea80e-0a97-4621-848f-08c25cf28f9f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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",
      "image/png": "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",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=128x128>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ll(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "a363ce16-1f6e-4d0a-b1f0-cb60eda20a8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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",
      "image/png": "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",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=128x128>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ll(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "id": "745a61ab-ce1b-4ca0-9db9-9daee4b1d813",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from diffusers import AutoencoderTiny\n",
    "vae = AutoencoderTiny.from_pretrained(\"madebyollin/taesdxl\", torch_dtype=torch.float32)\n",
    "vae = vae.to(\"cuda\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "8a237c1a-969a-414b-87a3-9b8c3a226116",
   "metadata": {},
   "outputs": [],
   "source": [
    "def vv(x):\n",
    "    pattern_noise = (torch.nn.functional.interpolate(noise_layer, scale_factor=4) - 0.5) * x\n",
    "\n",
    "    latents = torch.cat((pattern_noise, ones_layer, ones_layer, zero_layer), 1)\n",
    "    # print(latents.shape)\n",
    "    return vae.decode(latents)\n",
    "\n",
    "def vimg(latents):\n",
    "    lout = latents[0].detach().squeeze(0).cpu().numpy()\n",
    "    lout = (lout * 128) + 128\n",
    "    # print(lout.shape)\n",
    "    lout = lout.transpose(1, 2, 0) \n",
    "    # print(lout.shape)\n",
    "    return Image.fromarray(lout.astype(np.uint8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "78cadfdd-11fc-426f-b354-ec8ee8439664",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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",