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import logging
from dataclasses import dataclass
from functools import partial
from typing import Protocol
import matplotlib.pyplot as plt
import numpy as np
import scipy
import torch
import torch.nn.functional as F
from torch import Tensor, nn
from tqdm import trange
from .wn import WN
logger = logging.getLogger(__name__)
class VelocityField(Protocol):
def __call__(self, *, t: Tensor, ψt: Tensor, dt: Tensor) -> Tensor:
...
class Solver:
def __init__(
self,
method="midpoint",
nfe=32,
viz_name="solver",
viz_every=100,
mel_fn=None,
time_mapping_divisor=4,
verbose=False,
):
self.configurate_(nfe=nfe, method=method)
self.verbose = verbose
self.viz_every = viz_every
self.viz_name = viz_name
self._camera = None
self._mel_fn = mel_fn
self._time_mapping = partial(self.exponential_decay_mapping, n=time_mapping_divisor)
def configurate_(self, nfe=None, method=None):
if nfe is None:
nfe = self.nfe
if method is None:
method = self.method
if nfe == 1 and method in ("midpoint", "rk4"):
logger.warning(f"1 NFE is not supported for {method}, using euler method instead.")
method = "euler"
self.nfe = nfe
self.method = method
@property
def time_mapping(self):
return self._time_mapping
@staticmethod
def exponential_decay_mapping(t, n=4):
"""
Args:
n: target step
"""
def h(t, a):
return (a**t - 1) / (a - 1)
# Solve h(1/n) = 0.5
a = float(scipy.optimize.fsolve(lambda a: h(1 / n, a) - 0.5, x0=0))
t = h(t, a=a)
return t
@torch.no_grad()
def _maybe_camera_snap(self, *, ψt, t):
camera = self._camera
if camera is not None:
if ψt.shape[1] == 1:
# Waveform, b 1 t, plot every 100 samples
plt.subplot(211)
plt.plot(ψt.detach().cpu().numpy()[0, 0, ::100], color="blue")
if self._mel_fn is not None:
plt.subplot(212)
mel = self._mel_fn(ψt.detach().cpu().numpy()[0, 0])
plt.imshow(mel, origin="lower", interpolation="none")
elif ψt.shape[1] == 2:
# Complex
plt.subplot(121)
plt.imshow(
ψt.detach().cpu().numpy()[0, 0],
origin="lower",
interpolation="none",
)
plt.subplot(122)
plt.imshow(
ψt.detach().cpu().numpy()[0, 1],
origin="lower",
interpolation="none",
)
else:
# Spectrogram, b c t
plt.imshow(ψt.detach().cpu().numpy()[0], origin="lower", interpolation="none")
ax = plt.gca()
ax.text(0.5, 1.01, f"t={t:.2f}", transform=ax.transAxes, ha="center")
camera.snap()
@staticmethod
def _euler_step(t, ψt, dt, f: VelocityField):
return ψt + dt * f(t=t, ψt=ψt, dt=dt)
@staticmethod
def _midpoint_step(t, ψt, dt, f: VelocityField):
return ψt + dt * f(t=t + dt / 2, ψt=ψt + dt * f(t=t, ψt=ψt, dt=dt) / 2, dt=dt)
@staticmethod
def _rk4_step(t, ψt, dt, f: VelocityField):
k1 = f(t=t, ψt=ψt, dt=dt)
k2 = f(t=t + dt / 2, ψt=ψt + dt * k1 / 2, dt=dt)
k3 = f(t=t + dt / 2, ψt=ψt + dt * k2 / 2, dt=dt)
k4 = f(t=t + dt, ψt=ψt + dt * k3, dt=dt)
return ψt + dt * (k1 + 2 * k2 + 2 * k3 + k4) / 6
@property
def _step(self):
if self.method == "euler":
return self._euler_step
elif self.method == "midpoint":
return self._midpoint_step
elif self.method == "rk4":
return self._rk4_step
else:
raise ValueError(f"Unknown method: {self.method}")
def get_running_train_loop(self):
try:
# Lazy import
from ...utils.train_loop import TrainLoop
return TrainLoop.get_running_loop()
except ImportError:
return None
@property
def visualizing(self):
loop = self.get_running_train_loop()
if loop is None:
return
out_path = loop.make_current_step_viz_path(self.viz_name, ".gif")
return loop.global_step % self.viz_every == 0 and not out_path.exists()
def _reset_camera(self):
try:
from celluloid import Camera
self._camera = Camera(plt.figure())
except:
pass
def _maybe_dump_camera(self):
camera = self._camera
loop = self.get_running_train_loop()
if camera is not None and loop is not None:
animation = camera.animate()
out_path = loop.make_current_step_viz_path(self.viz_name, ".gif")
out_path.parent.mkdir(exist_ok=True, parents=True)
animation.save(out_path, writer="pillow", fps=4)
plt.close()
self._camera = None
@property
def n_steps(self):
n = self.nfe
if self.method == "euler":
pass
elif self.method == "midpoint":
n //= 2
elif self.method == "rk4":
n //= 4
else:
raise ValueError(f"Unknown method: {self.method}")
return n
def solve(self, f: VelocityField, ψ0: Tensor, t0=0.0, t1=1.0):
ts = self._time_mapping(np.linspace(t0, t1, self.n_steps + 1))
if self.visualizing:
self._reset_camera()
if self.verbose:
steps = trange(self.n_steps, desc="CFM inference")
else:
steps = range(self.n_steps)
ψt = ψ0
for i in steps:
dt = ts[i + 1] - ts[i]
t = ts[i]
self._maybe_camera_snap(ψt=ψt, t=t)
ψt = self._step(t=t, ψt=ψt, dt=dt, f=f)
self._maybe_camera_snap(ψt=ψt, t=ts[-1])
ψ1 = ψt
del ψt
self._maybe_dump_camera()
return ψ1
def __call__(self, f: VelocityField, ψ0: Tensor, t0=0.0, t1=1.0):
return self.solve(f=f, ψ0=ψ0, t0=t0, t1=t1)
class SinusodialTimeEmbedding(nn.Module):
def __init__(self, d_embed):
super().__init__()
self.d_embed = d_embed
assert d_embed % 2 == 0
def forward(self, t):
t = t.unsqueeze(-1) # ... 1
p = torch.linspace(0, 4, self.d_embed // 2).to(t)
while p.dim() < t.dim():
p = p.unsqueeze(0) # ... d/2
sin = torch.sin(t * 10**p)
cos = torch.cos(t * 10**p)
return torch.cat([sin, cos], dim=-1)
@dataclass(eq=False)
class CFM(nn.Module):
"""
This mixin is for general diffusion models.
ψ0 stands for the gaussian noise, and ψ1 is the data point.
Here we follow the CFM style:
The generation process (reverse process) is from t=0 to t=1.
The forward process is from t=1 to t=0.
"""
cond_dim: int
output_dim: int
time_emb_dim: int = 128
viz_name: str = "cfm"
solver_nfe: int = 32
solver_method: str = "midpoint"
time_mapping_divisor: int = 4
def __post_init__(self):
super().__init__()
self.solver = Solver(
viz_name=self.viz_name,
viz_every=1,
nfe=self.solver_nfe,
method=self.solver_method,
time_mapping_divisor=self.time_mapping_divisor,
)
self.emb = SinusodialTimeEmbedding(self.time_emb_dim)
self.net = WN(
input_dim=self.output_dim,
output_dim=self.output_dim,
local_dim=self.cond_dim,
global_dim=self.time_emb_dim,
)
def _perturb(self, ψ1: Tensor, t: Tensor | None = None):
"""
Perturb ψ1 to ψt.
"""
raise NotImplementedError
def _sample_ψ0(self, x: Tensor):
"""
Args:
x: (b c t), which implies the shape of ψ0
"""
shape = list(x.shape)
shape[1] = self.output_dim
if self.training:
g = None
else:
g = torch.Generator(device=x.device)
g.manual_seed(0) # deterministic sampling during eval
ψ0 = torch.randn(shape, device=x.device, dtype=x.dtype, generator=g)
return ψ0
@property
def sigma(self):
return 1e-4
def _to_ψt(self, *, ψ1: Tensor, ψ0: Tensor, t: Tensor):
"""
Eq (22)
"""
while t.dim() < ψ1.dim():
t = t.unsqueeze(-1)
μ = t * ψ1 + (1 - t) * ψ0
return μ + torch.randn_like(μ) * self.sigma
def _to_u(self, *, ψ1, ψ0: Tensor):
"""
Eq (21)
"""
return ψ1 - ψ0
def _to_v(self, *, ψt, x, t: float | Tensor):
"""
Args:
ψt: (b c t)
x: (b c t)
t: (b)
Returns:
v: (b c t)
"""
if isinstance(t, (float, int)):
t = torch.full(ψt.shape[:1], t).to(ψt)
t = t.clamp(0, 1) # [0, 1)
g = self.emb(t) # (b d)
v = self.net(ψt, l=x, g=g)
return v
def compute_losses(self, x, y, ψ0) -> dict:
"""
Args:
x: (b c t)
y: (b c t)
Returns:
losses: dict
"""
t = torch.rand(len(x), device=x.device, dtype=x.dtype)
t = self.solver.time_mapping(t)
if ψ0 is None:
ψ0 = self._sample_ψ0(x)
ψt = self._to_ψt(ψ1=y, t=t, ψ0=ψ0)
v = self._to_v(ψt=ψt, t=t, x=x)
u = self._to_u(ψ1=y, ψ0=ψ0)
losses = dict(l1=F.l1_loss(v, u))
return losses
@torch.inference_mode()
def sample(self, x, ψ0=None, t0=0.0):
"""
Args:
x: (b c t)
Returns:
y: (b ... t)
"""
if ψ0 is None:
ψ0 = self._sample_ψ0(x)
f = lambda t, ψt, dt: self._to_v(ψt=ψt, t=t, x=x)
ψ1 = self.solver(f=f, ψ0=ψ0, t0=t0)
return ψ1
def forward(self, x: Tensor, y: Tensor | None = None, ψ0: Tensor | None = None, t0=0.0):
if y is None:
y = self.sample(x, ψ0=ψ0, t0=t0)
else:
self.losses = self.compute_losses(x, y, ψ0=ψ0)
return y
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