Bu makala, o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z. Definition: Defini: O‘z O‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z Diffusion model O‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z. Autorlar o‘z o‘z o‘z o‘z: “ ”[1] Unbalanced thermodynamics (non-balance thermodynamics) o‘z o‘z o‘z. Unbalanced thermodynamics (non-balance thermodynamics) o‘z o‘z o‘z. Biz o‘z bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan. The essential idea, inspired by non-equilibrium statistical physics, is to systematically and slowly destroy structure in a data distribution through an iterative forward diffusion process. We then learn a reverse diffusion process that restores structure in data, yielding a highly flexible and tractable generative model of the data. O‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘. We start with a real, high-quality image and add noise to it in steps to arrive at pure noise. Basically, we want to destroy the structure in the non-random data distribution that exists at the start. Forward Diffusion Phase: Here, q is our forward process, the output of the forward process at time step t, is an input at time step t. N is a normal distribution with mean and variance. x_t x_(t-1) sqrt(1 - β_t) x_{t-1} β_tI [also called the schedule] here controls the amount of noise added at time step = t whose value ranges from 0→1. Depending on the type of schedule you use, you arrive at what is close to pure noise sooner or later. i.e. β_1,…,β_T is a variance schedule (that is either learned or fixed) which, if well-behaved, ensures that is almost an isotropic Gaussian at sufficiently large T. β_t x_T This is where the actual machine learning takes place. As the name suggests, we try to transform the noise back into a sample from the target distribution in this phase. i.e. the model is learning to denoise pure Gaussian noise into a clean image. Once the neural network has been trained, this ability can be used to generate new images out of Gaussian noise through step-by-step reverse diffusion. Reverse Diffusion Phase: Since one cannot readily estimate , we need to learn a model to approximate the conditional probabilities for the reverse diffusion process. q(x_(t-1)|x_t) p_theta We want to model the probability density of an earlier time step given the current. If we apply this reverse formula for all time steps T→0, we can trace our steps back to the original data distribution. The time step information is provided usually as positional embeddings to the model. It is worth mentioning here that the diffusion model at a given timestep to make it equivalent to the image at the start, and not just the delta between the current and previous time step. However, we only subtract part of it and move to the next step. That is how the diffusion process works. predicts the entire noise to be removed O‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z Bizga o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z Men o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z. Bir detalmatik mathematiki ekshadi, o‘z bu blogni qaytaradi [4]. destroys the structure in training data learns to recover passing randomly sampled noise through the “learned” denoising process Implementation: O‘zingiz: Biz o‘z o‘z o‘z o‘z. O‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z. Oksford Flowers102 data set O‘z gausian bilan da gausian, o‘z o‘z qilmadi qilmadi qilmadi qilmadi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi qilmidi. Forward phase: def linear_beta_schedule(timesteps, start=1e-4, end=2e-2): """Creates a linearly increasing noise schedule.""" return torch.linspace(start, end, timesteps) def get_idx_from_list(vals, t, x_shape): """ Returns a specific index t of a passed list of values vals. """ batch_size = t.shape[0] out = vals.gather(-1, t.cpu()) return out.reshape(batch_size, *((1,) * (len(x_shape) - 1))).to(t.device) def forward_diffusion_sample(x_0, t, device="cpu"): """ Takes an image and a timestep as input and returns the noisy version of it.""" noise = torch.randn_like(x_0) sqrt_alphas_cumprod_t = get_index_from_list(sqrt_alphas_cumprod, t, x_0.shape) sqrt_one_minus_alphas_cumprod_t = get_idx_from_list(sqrt_one_minus_alphas_cumprod, t, x_0.shape) return sqrt_alphas_cumprod_t.to(device) * x_0.to(device) + sqrt_one_minus_alphas_cumprod_t.to(device) * noise.to(device), noise.to(device) T = 300 # Total number of timesteps betas = linear_beta_schedule(T) # Precompute values for efficiency alphas = 1. - betas alphas_cumprod = torch.cumprod(alphas, dim=0) alphas_cumprod_prev = F.pad(alphas_cumprod[:-1], (1, 0), value=1.0) sqrt_recip_alphas = torch.sqrt(1. / alphas) sqrt_alphas_cumprod = torch.sqrt(alphas_cumprod) sqrt_one_minus_alphas_cumprod = torch.sqrt(1. - alphas_cumprod) posterior_variance = betas * (1. - alphas_cumprod_prev) / (1. - alphas_cumprod) Bu denozying faziydi, model o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z. U o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z. Reverse Diffusion Phase: ConvBlock class SinusoidalPositionEmbeddings(nn.Module): def __init__(self, dim): super().__init__() self.dim = dim def forward(self, t): half_dim = self.dim // 2 scale = math.log(10000) / (half_dim - 1) freqs = torch.exp(torch.arange(half_dim, device=t.device) * -scale) angles = t[:, None] * freqs[None, :] return torch.cat([angles.sin(), angles.cos()], dim=-1) class ConvBlock(nn.Module): def __init__(self, in_channels, out_channels, time_emb_dim, upsample=False): super().__init__() self.time_mlp = nn.Linear(time_emb_dim, out_channels) self.upsample = upsample self.conv1 = nn.Conv2d(in_channels * 2 if upsample else in_channels, out_channels, kernel_size=3, padding=1) self.transform = ( nn.ConvTranspose2d(out_channels, out_channels, kernel_size=4, stride=2, padding=1) if upsample else nn.Conv2d(out_channels, out_channels, kernel_size=4, stride=2, padding=1) ) self.conv2 = nn.Conv2d(out_channels, out_channels, kernel_size=3, padding=1) self.bn1 = nn.BatchNorm2d(out_channels) self.bn2 = nn.BatchNorm2d(out_channels) self.relu = nn.ReLU() def forward(self, x, t): h = self.bn1(self.relu(self.conv1(x))) time_emb = self.relu(self.time_mlp(t))[(..., ) + (None,) * 2] h = h + time_emb h = self.bn2(self.relu(self.conv2(h))) return self.transform(h) class SimpleUNet(nn.Module): """Simplified U-Net for denoising diffusion models.""" def __init__(self): super().__init__() image_channels = 3 down_channels = (64, 128, 256, 512, 1024) up_channels = (1024, 512, 256, 128, 64) output_channels = 3 time_emb_dim = 32 self.time_mlp = nn.Sequential( SinusoidalPositionEmbeddings(time_emb_dim), nn.Linear(time_emb_dim, time_emb_dim), nn.ReLU() ) self.init_conv = nn.Conv2d(image_channels, down_channels[0], kernel_size=3, padding=1) self.down_blocks = nn.ModuleList([ ConvBlock(down_channels[i], down_channels[i+1], time_emb_dim) for i in range(len(down_channels) - 1) ]) self.up_blocks = nn.ModuleList([ ConvBlock(up_channels[i], up_channels[i+1], time_emb_dim, upsample=True) for i in range(len(up_channels) - 1) ]) self.final_conv = nn.Conv2d(up_channels[-1], output_channels, kernel_size=1) def forward(self, x, t): t_emb = self.time_mlp(t) x = self.init_conv(x) skip_connections = [] for block in self.down_blocks: x = block(x, t_emb) skip_connections.append(x) for block in self.up_blocks: skip_x = skip_connections.pop() x = torch.cat([x, skip_x], dim=1) x = block(x, t_emb) return self.final_conv(x) model = SimpleUnet() MSE kaydi bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan bilan. def get_loss(model, x_0, t, device): x_noisy, noise = forward_diffusion_sample(x_0, t, device) noise_pred = model(x_noisy, t) return F.mse_loss(noise, noise_pred) Biz 300 epoch modelini qilmadi, bizga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga qilmayga q References: Deep Unsupervised Learning using Nonequilibrium Thermodynamics Sohl-Dickstein, J. et al.[2015] O‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z o‘z. GANs o‘z shadiq dhariwal və Nichol [2021] Bu o‘z blogni o‘zmatmatmatik bilan o‘zmatik o‘zmatik. Bu repository access to a collection of resources and papers on Diffusion Models. Bu blog o‘z. Bu repository
