def timestep_embedding(t: Tensor, dim, max_period=10000, time_factor: float = 1000.0):
    """
    Create sinusoidal timestep embeddings.
    :param t: a 1-D Tensor of N indices, one per batch element.
                      These may be fractional.
    :param dim: the dimension of the output.
    :param max_period: controls the minimum frequency of the embeddings.
    :return: an (N, D) Tensor of positional embeddings.
    """
    t = time_factor * t
    half = dim // 2
    freqs = torch.exp(-math.log(max_period) * torch.arange(start=0, end=half, dtype=torch.float32) / half).to(t.device)

    args = t[:, None].float() * freqs[None]
    embedding = torch.cat([torch.cos(args), torch.sin(args)], dim=-1)
    if dim % 2:
        embedding = torch.cat([embedding, torch.zeros_like(embedding[:, :1])], dim=-1)
    if torch.is_floating_point(t):
        embedding = embedding.to(t)
    return embedding

    Create sinusoidal timestep embeddings.
    :param t: a 1-D Tensor of N indices, one per batch element.
                      These may be fractional.
    :param dim: the dimension of the output.
    :param max_period: controls the minimum frequency of the embeddings.
    :return: an (N, D) Tensor of positional embeddings.
    
opensora/models/mmdit/layers.py