Moto Ndege: Ndege: Ndege: Ndege: Ndege: Ndege

Na makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makolinhot ya makol

Definition:

makolinhotDiffusion modelna na na na na na na na na na na na na na na na na na na na na na na na na na na na

Na na na na na na na na na na na na na na na na“Pamba la Pamba la Pamba la Pamba la Pamba la 100%”[1], makolinhot na :

Teya na teya na teya na teya na teya na teya na teya na teya na teya na teya na teya na teya na teya na teya na teya na teya na teya

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.

Pamba la Pamba la Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100%

• Forward Diffusion Phase: 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.

  Here, q is our forward process, x_t ​ the output of the forward process at time step t, x_(t-1)​ is an input at time step t. N is a normal distribution with sqrt(1 - β_t) x_{t-1} mean and β_tI variance.

  
  

  β_t [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 x_T is almost an isotropic Gaussian at sufficiently large T.

  
  

• Reverse Diffusion Phase: 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.

  Since one cannot readily estimate q(x_(t-1)|x_t), we need to learn a model p_theta to approximate the conditional probabilities for the reverse diffusion process.

  

  
  

• 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 predicts the entire noise to be removed 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.

  
  

Ekolali, Ekolali, Ekolalidestroys the structure in training datana ngomba ya gaussian, nalearns to recoverna na na na na na na na na na na napassing randomly sampled noise through the “learned” denoising process. Kofutela nzambe nzambe nzambe nzambe nzambe nzambe nzambe nzambe.

Implementation:

Na minoko kolekaOxford Flowers102 dataset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Forward phase:Saki ya ba gaussians na ba gaussians, na ba na lisis ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi ya baisi

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)

Reverse Diffusion Phase:Na na na na na na na na na na na na na na na na na na na na na na na na na na na naConvBlockKofutela ya nzambe ya nzambe ya nzambe ya nzambe ya nzambe ya nzambe ya nzambe ya nzambe ya nzambe ya nzambe ya nzambe ya nzambe ya nzambe.

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()

ETENI YA 6 - LELO

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)

Eko bebisa ba miso ya modelini ya 300 epochs, mpe o komona mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula mbula

References:

1. Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba
2. Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la [2020]
3. Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la Pamba [2021]
4. Pamba la Pamba la Pamba la Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100% ya Pamba la 100%.
5. Pamba la Pamba la Pamba la Pamba la Pamba la Pamba la 100%