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from typing import Optional
import torch
from torch import FloatTensor, LongTensor, Size, Tensor
from prior import generate_beta_tensor
class OuterInterpolatedAttnProcessor:
r"""
Personalized processor for performing outer attention interpolation.
The attention output of interpolated image is obtained by:
(1 - t) * Q_t * K_1 * V_1 + t * Q_t * K_m * V_m;
If fused with self-attention:
(1 - t) * Q_t * [K_1, K_t] * [V_1, V_t] + t * Q_t * [K_m, K_t] * [V_m, V_t];
"""
def __init__(
self,
t: Optional[float] = None,
size: int = 7,
is_fused: bool = False,
alpha: float = 1,
beta: float = 1,
):
"""
t: float, interpolation point between 0 and 1, if specified, size is set to 3
"""
if t is None:
ts = generate_beta_tensor(size, alpha=alpha, beta=beta)
ts[0], ts[-1] = 0, 1
else:
assert t > 0 and t < 1, "t must be between 0 and 1"
ts = [0, t, 1]
ts = torch.tensor(ts)
size = 3
self.size = size
self.coef = ts
self.is_fused = is_fused
def __call__(
self,
attn,
hidden_states: torch.FloatTensor,
encoder_hidden_states: Optional[torch.FloatTensor] = None,
attention_mask: Optional[torch.FloatTensor] = None,
temb: Optional[torch.FloatTensor] = None,
) -> torch.Tensor:
residual = hidden_states
if attn.spatial_norm is not None:
hidden_states = attn.spatial_norm(hidden_states, temb)
input_ndim = hidden_states.ndim
if input_ndim == 4:
batch_size, channel, height, width = hidden_states.shape
hidden_states = hidden_states.view(
batch_size, channel, height * width
).transpose(1, 2)
batch_size, sequence_length, _ = (
hidden_states.shape
if encoder_hidden_states is None
else encoder_hidden_states.shape
)
attention_mask = attn.prepare_attention_mask(
attention_mask, sequence_length, batch_size
)
if attn.group_norm is not None:
hidden_states = attn.group_norm(hidden_states.transpose(1, 2)).transpose(
1, 2
)
query = attn.to_q(hidden_states)
query = attn.head_to_batch_dim(query)
if encoder_hidden_states is None:
encoder_hidden_states = hidden_states
elif attn.norm_cross:
encoder_hidden_states = attn.norm_encoder_hidden_states(
encoder_hidden_states
)
key = attn.to_k(encoder_hidden_states)
value = attn.to_v(encoder_hidden_states)
# Specify the first and last key and value
key_begin = key[0:1]
key_end = key[-1:]
value_begin = value[0:1]
value_end = value[-1:]
key_begin = torch.cat([key_begin] * (self.size))
key_end = torch.cat([key_end] * (self.size))
value_begin = torch.cat([value_begin] * (self.size))
value_end = torch.cat([value_end] * (self.size))
key_begin = attn.head_to_batch_dim(key_begin)
value_begin = attn.head_to_batch_dim(value_begin)
key_end = attn.head_to_batch_dim(key_end)
value_end = attn.head_to_batch_dim(value_end)
# Fused with self-attention
if self.is_fused:
key = attn.head_to_batch_dim(key)
value = attn.head_to_batch_dim(value)
key_end = torch.cat([key, key_end], dim=-2)
value_end = torch.cat([value, value_end], dim=-2)
key_begin = torch.cat([key, key_begin], dim=-2)
value_begin = torch.cat([value, value_begin], dim=-2)
attention_probs_end = attn.get_attention_scores(query, key_end, attention_mask)
hidden_states_end = torch.bmm(attention_probs_end, value_end)
hidden_states_end = attn.batch_to_head_dim(hidden_states_end)
attention_probs_begin = attn.get_attention_scores(
query, key_begin, attention_mask
)
hidden_states_begin = torch.bmm(attention_probs_begin, value_begin)
hidden_states_begin = attn.batch_to_head_dim(hidden_states_begin)
# Apply outer interpolation on attention
coef = self.coef.reshape(-1, 1, 1)
coef = coef.to(key.device, key.dtype)
hidden_states = (1 - coef) * hidden_states_begin + coef * hidden_states_end
hidden_states = attn.to_out[0](hidden_states)
hidden_states = attn.to_out[1](hidden_states)
if input_ndim == 4:
hidden_states = hidden_states.transpose(-1, -2).reshape(
batch_size, channel, height, width
)
if attn.residual_connection:
hidden_states = hidden_states + residual
hidden_states = hidden_states / attn.rescale_output_factor
return hidden_states
class InnerInterpolatedAttnProcessor:
r"""
Personalized processor for performing inner attention interpolation.
The attention output of interpolated image is obtained by:
(1 - t) * Q_t * K_1 * V_1 + t * Q_t * K_m * V_m;
If fused with self-attention:
(1 - t) * Q_t * [K_1, K_t] * [V_1, V_t] + t * Q_t * [K_m, K_t] * [V_m, V_t];
"""
def __init__(
self,
t: Optional[float] = None,
size: int = 7,
is_fused: bool = False,
alpha: float = 1,
beta: float = 1,
):
"""
t: float, interpolation point between 0 and 1, if specified, size is set to 3
"""
if t is None:
ts = generate_beta_tensor(size, alpha=alpha, beta=beta)
ts[0], ts[-1] = 0, 1
else:
assert t > 0 and t < 1, "t must be between 0 and 1"
ts = [0, t, 1]
ts = torch.tensor(ts)
size = 3
self.size = size
self.coef = ts
self.is_fused = is_fused
def __call__(
self,
attn,
hidden_states: torch.FloatTensor,
encoder_hidden_states: Optional[torch.FloatTensor] = None,
attention_mask: Optional[torch.FloatTensor] = None,
temb: Optional[torch.FloatTensor] = None,
) -> torch.Tensor:
residual = hidden_states
if attn.spatial_norm is not None:
hidden_states = attn.spatial_norm(hidden_states, temb)
input_ndim = hidden_states.ndim
if input_ndim == 4:
batch_size, channel, height, width = hidden_states.shape
hidden_states = hidden_states.view(
batch_size, channel, height * width
).transpose(1, 2)
batch_size, sequence_length, _ = (
hidden_states.shape
if encoder_hidden_states is None
else encoder_hidden_states.shape
)
attention_mask = attn.prepare_attention_mask(
attention_mask, sequence_length, batch_size
)
if attn.group_norm is not None:
hidden_states = attn.group_norm(hidden_states.transpose(1, 2)).transpose(
1, 2
)
query = attn.to_q(hidden_states)
query = attn.head_to_batch_dim(query)
if encoder_hidden_states is None:
encoder_hidden_states = hidden_states
elif attn.norm_cross:
encoder_hidden_states = attn.norm_encoder_hidden_states(
encoder_hidden_states
)
key = attn.to_k(encoder_hidden_states)
value = attn.to_v(encoder_hidden_states)
# Specify the first and last key and value
key_start = key[0:1]
key_end = key[-1:]
value_start = value[0:1]
value_end = value[-1:]
key_start = torch.cat([key_start] * (self.size))
key_end = torch.cat([key_end] * (self.size))
value_start = torch.cat([value_start] * (self.size))
value_end = torch.cat([value_end] * (self.size))
# Apply inner interpolation on attention
coef = self.coef.reshape(-1, 1, 1)
coef = coef.to(key.device, key.dtype)
key_cross = (1 - coef) * key_start + coef * key_end
value_cross = (1 - coef) * value_start + coef * value_end
key_cross = attn.head_to_batch_dim(key_cross)
value_cross = attn.head_to_batch_dim(value_cross)
# Fused with self-attention
if self.is_fused:
key = attn.head_to_batch_dim(key)
value = attn.head_to_batch_dim(value)
key_cross = torch.cat([key, key_cross], dim=-2)
value_cross = torch.cat([value, value_cross], dim=-2)
attention_probs = attn.get_attention_scores(query, key_cross, attention_mask)
hidden_states = torch.bmm(attention_probs, value_cross)
hidden_states = attn.batch_to_head_dim(hidden_states)
hidden_states = attn.to_out[0](hidden_states)
hidden_states = attn.to_out[1](hidden_states)
if input_ndim == 4:
hidden_states = hidden_states.transpose(-1, -2).reshape(
batch_size, channel, height, width
)
if attn.residual_connection:
hidden_states = hidden_states + residual
hidden_states = hidden_states / attn.rescale_output_factor
return hidden_states
def linear_interpolation(
l1: FloatTensor, l2: FloatTensor, ts: Optional[FloatTensor] = None, size: int = 5
) -> FloatTensor:
"""
Linear interpolation
Args:
l1: Starting vector: (1, *)
l2: Final vector: (1, *)
ts: FloatTensor, interpolation points between 0 and 1
size: int, number of interpolation points including l1 and l2
Returns:
Interpolated vectors: (size, *)
"""
assert l1.shape == l2.shape, "shapes of l1 and l2 must match"
res = []
if ts is not None:
for t in ts:
li = torch.lerp(l1, l2, t)
res.append(li)
else:
for i in range(size):
t = i / (size - 1)
li = torch.lerp(l1, l2, t)
res.append(li)
res = torch.cat(res, dim=0)
return res
def spherical_interpolation(l1: FloatTensor, l2: FloatTensor, size=5) -> FloatTensor:
"""
Spherical interpolation
Args:
l1: Starting vector: (1, *)
l2: Final vector: (1, *)
size: int, number of interpolation points including l1 and l2
Returns:
Interpolated vectors: (size, *)
"""
assert l1.shape == l2.shape, "shapes of l1 and l2 must match"
res = []
for i in range(size):
t = i / (size - 1)
li = slerp(l1, l2, t)
res.append(li)
res = torch.cat(res, dim=0)
return res
def slerp(v0: FloatTensor, v1: FloatTensor, t, threshold=0.9995):
"""
Spherical linear interpolation
Args:
v0: Starting vector
v1: Final vector
t: Float value between 0.0 and 1.0
threshold: Threshold for considering the two vectors as
colinear. Not recommended to alter this.
Returns:
Interpolation vector between v0 and v1
"""
assert v0.shape == v1.shape, "shapes of v0 and v1 must match"
# Normalize the vectors to get the directions and angles
v0_norm: FloatTensor = torch.norm(v0, dim=-1)
v1_norm: FloatTensor = torch.norm(v1, dim=-1)
v0_normed: FloatTensor = v0 / v0_norm.unsqueeze(-1)
v1_normed: FloatTensor = v1 / v1_norm.unsqueeze(-1)
# Dot product with the normalized vectors
dot: FloatTensor = (v0_normed * v1_normed).sum(-1)
dot_mag: FloatTensor = dot.abs()
# if dp is NaN, it's because the v0 or v1 row was filled with 0s
# If absolute value of dot product is almost 1, vectors are ~colinear, so use torch.lerp
gotta_lerp: LongTensor = dot_mag.isnan() | (dot_mag > threshold)
can_slerp: LongTensor = ~gotta_lerp
t_batch_dim_count: int = max(0, t.dim() - v0.dim()) if isinstance(t, Tensor) else 0
t_batch_dims: Size = (
t.shape[:t_batch_dim_count] if isinstance(t, Tensor) else Size([])
)
out: FloatTensor = torch.zeros_like(v0.expand(*t_batch_dims, *[-1] * v0.dim()))
# if no elements are lerpable, our vectors become 0-dimensional, preventing broadcasting
if gotta_lerp.any():
lerped: FloatTensor = torch.lerp(v0, v1, t)
out: FloatTensor = lerped.where(gotta_lerp.unsqueeze(-1), out)
# if no elements are slerpable, our vectors become 0-dimensional, preventing broadcasting
if can_slerp.any():
# Calculate initial angle between v0 and v1
theta_0: FloatTensor = dot.arccos().unsqueeze(-1)
sin_theta_0: FloatTensor = theta_0.sin()
# Angle at timestep t
theta_t: FloatTensor = theta_0 * t
sin_theta_t: FloatTensor = theta_t.sin()
# Finish the slerp algorithm
s0: FloatTensor = (theta_0 - theta_t).sin() / sin_theta_0
s1: FloatTensor = sin_theta_t / sin_theta_0
slerped: FloatTensor = s0 * v0 + s1 * v1
out: FloatTensor = slerped.where(can_slerp.unsqueeze(-1), out)
return out
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