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{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"id": "02b6d28f", | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import numpy as np\n", | |
"import jax\n", | |
"from jax import numpy as jnp\n", | |
"import matplotlib.pyplot as plt" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "1a777fd0", | |
"metadata": {}, | |
"source": [ | |
"## データの生成" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"id": "7cca8a8b", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"[<matplotlib.lines.Line2D at 0x12631bd90>]" | |
] | |
}, | |
"execution_count": 2, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 640x480 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"num_gaussians = 5\n", | |
"radius = 2\n", | |
"variance = 0.05\n", | |
"num_samples = 256\n", | |
"\n", | |
"thetas = jnp.linspace(0, 2 * jnp.pi * (1 - 1/num_gaussians), num_gaussians)\n", | |
"mus = radius * jnp.concatenate((jnp.cos(thetas)[:, None], jnp.sin(thetas)[:, None]), axis=1)\n", | |
"\n", | |
"rng = jax.random.PRNGKey(0)\n", | |
"indices = jax.random.randint(rng, shape=(num_samples, ), minval=0, maxval=num_gaussians)\n", | |
"x = mus[indices] + jnp.sqrt(variance) * jax.random.normal(rng, shape=(num_samples, 2))\n", | |
"\n", | |
"plt.plot(x[:, 0], x[:, 1], 'o')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "697e3bf6", | |
"metadata": {}, | |
"source": [ | |
"## 順過程" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"id": "534da35d", | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"from functools import partial, lru_cache\n", | |
"from collections.abc import Callable\n", | |
"\n", | |
"\n", | |
"class Scheduler:\n", | |
" def __call__(self, timestep: int) -> float:\n", | |
" raise NotImplementedError\n", | |
"\n", | |
" \n", | |
"class LinearScheduler(Scheduler):\n", | |
" def __init__(self, coef: float = 1.0, bias: float = 0.0) -> None:\n", | |
" self._coef = coef\n", | |
" self._bias = bias\n", | |
" \n", | |
" def __call__(self, timestep: int | float) -> float:\n", | |
" return self._coef * timestep + self._bias" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"id": "91b4ec66", | |
"metadata": { | |
"scrolled": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 1500x300 with 4 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"T = 16\n", | |
"beta = jnp.vectorize(LinearScheduler(coef=0.15 / T))\n", | |
"alpha = lambda t: 1.0 - beta(t)\n", | |
"alphabar = jnp.cumprod(alpha(jnp.arange(T + 1)))\n", | |
"\n", | |
"num_figures = 4\n", | |
"plt.figure(figsize=(15, 3))\n", | |
"checkpoints = [round(int(x)) for x in jnp.linspace(0, T, num_figures)]\n", | |
"for t in range(T + 1):\n", | |
" x_t = jnp.sqrt(alphabar[t]) * x + jnp.sqrt(1 - alphabar[t]) * jax.random.normal(rng, shape=x.shape)\n", | |
" if t in checkpoints:\n", | |
" plt.subplot(1, num_figures, checkpoints.index(t) + 1)\n", | |
" plt.title(f\"{t=}\")\n", | |
" plt.plot(x_t[:, 0], x_t[:, 1], 'o')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "116f8fd1", | |
"metadata": {}, | |
"source": [ | |
"## 逆過程の学習" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"id": "c83d9956", | |
"metadata": { | |
"scrolled": false | |
}, | |
"outputs": [], | |
"source": [ | |
"import random\n", | |
"from typing import Sequence\n", | |
"\n", | |
"import flax.linen as nn\n", | |
"\n", | |
"\n", | |
"class AddTimestepEncoding(nn.Module):\n", | |
" @nn.compact\n", | |
" def __call__(self, x: jnp.ndarray, t: jnp.ndarray) -> jnp.ndarray:\n", | |
" num_features = x.shape[-1]\n", | |
" timestep_embeddings = t[:, None] / (10000 ** (2 * jnp.arange(num_features)[None, :] / num_features))\n", | |
" timestep_embeddings = timestep_embeddings.at[:, 0::2].set(jnp.sin(timestep_embeddings[:, 0::2]))\n", | |
" timestep_embeddings = timestep_embeddings.at[:, 1::2].set(jnp.cos(timestep_embeddings[:, 1::2]))\n", | |
" return x + timestep_embeddings\n", | |
"\n", | |
"\n", | |
"class MLP(nn.Module):\n", | |
" hidden_dims: Sequence[int]\n", | |
" use_layernorm: bool = False\n", | |
"\n", | |
" @nn.compact\n", | |
" def __call__(self, x: jnp.ndarray) -> jnp.ndarray:\n", | |
" for dim in self.hidden_dims[:-1]:\n", | |
" x = nn.gelu(nn.Dense(dim)(x))\n", | |
" if self.use_layernorm:\n", | |
" x = nn.LayerNorm()(x)\n", | |
" x = nn.Dense(self.hidden_dims[-1])(x)\n", | |
" return x\n", | |
"\n", | |
"\n", | |
"class Diffuser(nn.Module):\n", | |
" hidden_dim: int\n", | |
" num_layers: int\n", | |
" use_layernorm: bool = False\n", | |
" \n", | |
" @nn.compact\n", | |
" def __call__(self, x: jnp.ndarray, t: jnp.ndarray) -> jnp.ndarray:\n", | |
" _, input_dim = x.shape\n", | |
" h = AddTimestepEncoding()(x, t)\n", | |
" h = MLP(hidden_dims=[self.hidden_dim] * self.num_layers, use_layernorm=self.use_layernorm)(h)\n", | |
" h = nn.Dense(input_dim)(h) + x\n", | |
" return h\n", | |
"\n", | |
"\n", | |
"model = Diffuser(hidden_dim=8, num_layers=3, use_layernorm=True)\n", | |
"params = model.init(rng, x, jnp.zeros((len(x),), dtype=jnp.int32))\n", | |
"\n", | |
"\n", | |
"@jax.jit\n", | |
"def loss_fn(params, rng, x: jnp.ndarray):\n", | |
" batch_size, _ = x.shape\n", | |
" eps = jax.random.uniform(rng)\n", | |
" t = jax.random.randint(rng, shape=(batch_size, ), minval=1, maxval=T).astype(jnp.int32)\n", | |
" ab = alphabar[t, None]\n", | |
" xt = jnp.sqrt(ab) * x + jnp.sqrt(1 - ab) * eps\n", | |
" eps_theta = model.apply(params, xt, t)\n", | |
" return jnp.sum((eps - eps_theta) ** 2) / batch_size" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"id": "b1764d18", | |
"metadata": { | |
"scrolled": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"epoch=9999 \t loss=DeviceArray(0.58586, dtype=float32)32)\r" | |
] | |
}, | |
{ | |
"data": { | |
"text/plain": [ | |
"[<matplotlib.lines.Line2D at 0x14a325a50>]" | |
] | |
}, | |
"execution_count": 6, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 640x480 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"import optax\n", | |
"\n", | |
"max_epochs = 10000\n", | |
"\n", | |
"optimizer = optax.yogi(learning_rate=1e-4)\n", | |
"opt_state = optimizer.init(params)\n", | |
"losses = []\n", | |
"\n", | |
"for epoch in range(max_epochs):\n", | |
" rng, subkey = jax.random.split(rng)\n", | |
" loss, grads = jax.value_and_grad(loss_fn)(params, subkey, x)\n", | |
" updates, opt_state = optimizer.update(grads, opt_state, params)\n", | |
" params = optax.apply_updates(params, updates)\n", | |
" losses.append(float(loss))\n", | |
" print(f\"{epoch=} \\t {loss=}\", end=\"\\r\")\n", | |
"\n", | |
"plt.plot(losses)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "512e251b", | |
"metadata": {}, | |
"source": [ | |
"## サンプリング" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"id": "44ea5af7", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 1500x300 with 4 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"num_samples = 256\n", | |
"\n", | |
"num_figures = 4\n", | |
"plt.figure(figsize=(15, 3))\n", | |
"checkpoints = [round(int(x)) for x in jnp.linspace(0, T, num_figures)]\n", | |
"\n", | |
"x_sample = jax.random.normal(rng, shape=(num_samples, x.shape[-1]))\n", | |
"plt.subplot(1, num_figures, checkpoints.index(T) + 1)\n", | |
"plt.title(f\"t={T}\")\n", | |
"plt.plot(x_sample[:, 0], x_sample[:, 1], 'o')\n", | |
"\n", | |
"for t in range(T, 0, -1):\n", | |
" rng, subkey = jax.random.split(rng)\n", | |
" z = jax.random.normal(subkey, shape=x_sample.shape) if t > 1 else jnp.zeros(x_sample.shape)\n", | |
" eps_theta = model.apply(params, x_sample, t * jnp.ones((num_samples, ), dtype=jnp.int32))\n", | |
" sigma = jnp.sqrt(beta(t) * (1 - alphabar[t - 1]) / (1 - alphabar[t]))\n", | |
" x_sample = (1.0 / jnp.sqrt(alpha(t))) * (x_sample - (beta(t) / jnp.sqrt(1 - alphabar[t])) * eps_theta) + sigma * z\n", | |
" \n", | |
" t = t - 1\n", | |
" if t in checkpoints:\n", | |
" plt.subplot(1, num_figures, checkpoints.index(t) + 1)\n", | |
" plt.title(f\"{t=}\")\n", | |
" plt.plot(x_sample[:, 0], x_sample[:, 1], 'o')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"id": "328f5d52", | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3 (ipykernel)", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.10.8" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 5 | |
} |
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