from collections.abc import Sequence, Mapping
from typing import Any, Literal, Callable
import keras
from keras import ops
from bayesflow.types import Tensor, Shape
from bayesflow.utils import (
expand_right_as,
find_network,
integrate,
integrate_stochastic,
jacobian_trace,
layer_kwargs,
logging,
linsolve_batched,
maybe_mask_tensor,
random_mask,
randomly_mask_along_axis,
resolve_seed,
weighted_mean,
DETERMINISTIC_METHODS,
STOCHASTIC_METHODS,
)
from bayesflow.utils.serialization import serialize, serializable
from .schedules.noise_schedule import NoiseSchedule
from .dispatch import find_noise_schedule
from ...inference import InferenceNetwork
from ...defaults import TIME_MLP_DEFAULTS, DIFFUSION_INTEGRATE_DEFAULTS
[docs]
@serializable("bayesflow.networks")
class DiffusionModel(InferenceNetwork):
"""Score-based diffusion model for simulation-based inference (SBI).
Implements a score-based diffusion model with configurable subnet architecture,
noise schedule, and prediction/loss types for amortized SBI as described in [1].
The diffusion model allows for post-hoc guidance (see [1]) and composition [2],
implementing, stabilizing, and scaling initial ideas from [3] and [4].
Note that score-based diffusion is the most sluggish of all available samplers,
so expect slower inference times than flow matching and much slower than
normalizing flows.
Parameters
----------
subnet : str, type, or keras.Layer, optional
A neural network type for the diffusion model, will be instantiated using
*subnet_kwargs*. If a string is provided, it should be a registered name
(e.g., ``"time_mlp"``). If a type or ``keras.Layer`` is provided, it will
be directly instantiated with the given *subnet_kwargs*. Any subnet must
accept a tuple of tensors ``(target, time, conditions)``.
noise_schedule : {'edm', 'cosine'} or NoiseSchedule or type, optional
Noise schedule controlling the diffusion dynamics. Can be a string
identifier, a schedule class, or a pre-initialised schedule instance.
Default is ``"edm"``.
prediction_type : {'velocity', 'noise', 'F', 'x', 'score', 'potential'}, optional
Output format of the model's prediction. Default is ``"F"``.
loss_type : {'velocity', 'noise', 'F'}, optional
Loss function used to train the model. Default is ``"noise"``.
subnet_kwargs : dict[str, Any], optional
Additional keyword arguments passed to the subnet constructor.
schedule_kwargs : dict[str, Any], optional
Additional keyword arguments passed to the noise schedule constructor.
integrate_kwargs : dict[str, Any], optional
Configuration dictionary for the ODE/SDE integrator used at inference time.
drop_cond_prob : float, optional
Probability of dropping conditions during training (i.e., classifier-free guidance).
Default is 0.0.
drop_target_prob : float, optional
Probability of dropping target values during training (i.e., learning arbitrary
distributions). Default is 0.0.
**kwargs
Additional keyword arguments passed to the base ``InferenceNetwork``.
References
----------
[1] Arruda, J., Bracher, N., Köthe, U., Hasenauer, J., & Radev, S. T. (2025).
Diffusion Models in Simulation-Based Inference: A Tutorial Review.
arXiv preprint arXiv:2512.20685.
[2] Arruda et al., (2025). Compositional amortized inference for large-scale hierarchical Bayesian models.
https://arxiv.org/abs/2505.14429
[3] Geffner et al., (2023). Compositional score modeling for simulation-based inference.
https://arxiv.org/abs/2209.14249
[4] Linhart et al., (2024). Diffusion posterior sampling for simulation-based inference in tall data settings.
https://arxiv.org/abs/2404.07593
"""
def __init__(
self,
*,
subnet: str | type | keras.Layer = "time_mlp",
noise_schedule: Literal["edm", "cosine"] | NoiseSchedule | type = "edm",
prediction_type: Literal["velocity", "noise", "F", "x", "score", "potential"] = "F",
loss_type: Literal["velocity", "noise", "F"] = "noise",
subnet_kwargs: dict[str, Any] = None,
schedule_kwargs: dict[str, Any] = None,
integrate_kwargs: dict[str, Any] = None,
drop_cond_prob: float = 0.0,
drop_target_prob: float = 0.0,
**kwargs,
):
super().__init__(base_distribution="normal", **kwargs)
if prediction_type not in ["noise", "velocity", "F", "x", "score", "potential"]:
raise ValueError(f"Unknown prediction type: {prediction_type}")
if loss_type not in ["noise", "velocity", "F"]:
raise ValueError(f"Unknown loss type: {loss_type}")
if loss_type != "noise":
logging.warning(
"The standard schedules have weighting functions defined for the noise prediction loss. "
"You might want to replace them if you are using a different loss function."
)
self._prediction_type = prediction_type
self._loss_type = loss_type
schedule_kwargs = schedule_kwargs or {}
self.noise_schedule = find_noise_schedule(noise_schedule, **schedule_kwargs)
self.noise_schedule.validate()
self.integrate_kwargs = DIFFUSION_INTEGRATE_DEFAULTS | (integrate_kwargs or {})
self.seed_generator = keras.random.SeedGenerator()
subnet_kwargs = subnet_kwargs or {}
if subnet == "time_mlp":
subnet_kwargs = TIME_MLP_DEFAULTS | subnet_kwargs
self.subnet = find_network(subnet, **subnet_kwargs)
self.output_projector = None
self.drop_cond_prob = drop_cond_prob
self.unconditional_mode = False
self.drop_target_prob = drop_target_prob
self.compositional_bridge_d0 = 1.0
self.compositional_bridge_d1 = 1.0
[docs]
def compute_metrics(
self,
x: Tensor | Sequence[Tensor],
conditions: Tensor = None,
sample_weight: Tensor = None,
stage: str = "training",
**kwargs,
) -> dict[str, Tensor]:
subnet_kwargs = self._collect_mask_kwargs(self._SUBNET_MASK_KEYS, kwargs)
training = stage == "training"
noise_schedule_training_stage = stage == "training" or stage == "validation"
if conditions is not None:
conditions = randomly_mask_along_axis(conditions, self.drop_cond_prob, seed_generator=self.seed_generator)
# Sample training diffusion time as a low discrepancy sequence to decrease variance
u0 = keras.random.uniform(shape=(1,), dtype=ops.dtype(x), seed=self.seed_generator)
i = ops.arange(0, ops.shape(x)[0], dtype=ops.dtype(x))
t = (u0 + i / ops.cast(ops.shape(x)[0], dtype=ops.dtype(x))) % 1
# Calculate the noise level
log_snr_t = self.noise_schedule.get_log_snr(t, training=noise_schedule_training_stage)
log_snr_t = expand_right_as(log_snr_t, x)
alpha_t, sigma_t = self.noise_schedule.get_alpha_sigma(log_snr_t=log_snr_t)
weights_for_snr = self.noise_schedule.get_weights_for_snr(log_snr_t=log_snr_t)
# Generate noise vector
eps_t = keras.random.normal(ops.shape(x), dtype=ops.dtype(x), seed=self.seed_generator)
# Diffuse x to get noisy input to the network
diffused_x = alpha_t * x + sigma_t * eps_t
# Generate optional target dropout mask
mask_x = random_mask(ops.shape(x), self.drop_target_prob, self.seed_generator)
diffused_x = maybe_mask_tensor(diffused_x, mask=mask_x, replacement=x)
# Obtain output of the network and transform to prediction of the clean signal x
norm_log_snr_t = self._transform_log_snr(log_snr_t)
if self._prediction_type == "potential":
pred = self._compute_grad_of_potential(
xz=diffused_x, norm_log_snr=norm_log_snr_t, conditions=conditions, training=training, **subnet_kwargs
)
x_pred = self.convert_prediction_to_x(
pred=pred,
z=diffused_x,
alpha_t=alpha_t,
sigma_t=sigma_t,
log_snr_t=log_snr_t,
prediction_type="velocity",
)
else:
subnet_out = self.subnet((diffused_x, norm_log_snr_t, conditions), training=training, **subnet_kwargs)
pred = self.output_projector(subnet_out)
x_pred = self.convert_prediction_to_x(
pred=pred,
z=diffused_x,
alpha_t=alpha_t,
sigma_t=sigma_t,
log_snr_t=log_snr_t,
prediction_type=self._prediction_type,
)
# Finally, compute the loss according to the configured loss type. Note that the standard weighting
# functions are defined for the noise prediction loss, so if you use a different loss type, you might want
# to adjust the weighting accordingly.
match self._loss_type:
case "noise":
noise_pred = (diffused_x - alpha_t * x_pred) / sigma_t
loss = weights_for_snr * ops.mean(mask_x * (noise_pred - eps_t) ** 2, axis=-1)
case "velocity":
velocity_pred = (alpha_t * diffused_x - x_pred) / sigma_t
v_t = alpha_t * eps_t - sigma_t * x
loss = weights_for_snr * ops.mean(mask_x * (velocity_pred - v_t) ** 2, axis=-1)
case "F":
sigma_data = self.noise_schedule.sigma_data if hasattr(self.noise_schedule, "sigma_data") else 1.0
x1 = ops.sqrt(ops.exp(-log_snr_t) + sigma_data**2) / (ops.exp(-log_snr_t / 2) * sigma_data)
x2 = (sigma_data * alpha_t) / (ops.exp(-log_snr_t / 2) * ops.sqrt(ops.exp(-log_snr_t) + sigma_data**2))
f_pred = x1 * x_pred - x2 * diffused_x
f_t = x1 * x - x2 * diffused_x
loss = weights_for_snr * ops.mean(mask_x * (f_pred - f_t) ** 2, axis=-1)
case _:
raise ValueError(f"Unknown loss type: {self._loss_type}")
loss = weighted_mean(loss, sample_weight)
return {"loss": loss}
[docs]
def build(self, xz_shape: Shape, conditions_shape: Shape = None):
if self.built:
return
self.base_distribution.build(xz_shape)
units = 1 if self._prediction_type == "potential" else xz_shape[-1]
self.output_projector = keras.layers.Dense(units=units, bias_initializer="zeros")
# construct input shape for subnet and subnet projector
time_shape = (xz_shape[0], 1)
self.subnet.build((xz_shape, time_shape, conditions_shape))
out_shape = self.subnet.compute_output_shape((xz_shape, time_shape, conditions_shape))
self.output_projector.build(out_shape)
[docs]
def get_config(self):
base_config = super().get_config()
base_config = layer_kwargs(base_config)
config = {
"subnet": self.subnet,
"noise_schedule": self.noise_schedule,
"prediction_type": self._prediction_type,
"loss_type": self._loss_type,
"integrate_kwargs": self.integrate_kwargs,
"drop_cond_prob": self.drop_cond_prob,
"drop_target_prob": self.drop_target_prob,
}
return base_config | serialize(config)
[docs]
def guidance_constraint_term(
self,
x: Tensor,
time: Tensor,
constraints: Callable | Sequence[Callable],
guidance_strength: float = 1.0,
scaling_function: Callable | None = None,
reduce: Literal["sum", "mean"] = "sum",
) -> Tensor:
"""
Backend-agnostic implementation of:
`∇_x Σ_k log sigmoid( -s(t) * c_k(x) )`
Parameters
----------
x : Tensor
The denoised target at time t.
time : Tensor
The time corresponding to x.
constraints : Callable or Sequence[Callable]
A single constraint function or a list/tuple of constraint functions.
Each function should take x as input and return a tensor of constraint values.
guidance_strength : float, optional
A positive scaling factor for the guidance term. Default is 1.0.
scaling_function : Callable, optional
A function that takes time t as input and returns a scaling factor s(t).
If None, a default scaling based on the noise schedule is used. Default is None.
reduce : {'sum', 'mean'}, optional
Method to reduce the log-probabilities from multiple constraints. Default is 'sum'.
Returns
-------
Tensor
The computed guidance term of the same shape as zt.
"""
if not isinstance(constraints, Sequence):
constraints = [constraints]
if scaling_function is None:
def scaling_function(t: Tensor):
log_snr = self.noise_schedule.get_log_snr(t, training=False)
alpha_t, sigma_t = self.noise_schedule.get_alpha_sigma(log_snr)
return ops.square(alpha_t) / ops.square(sigma_t)
def objective_fn(z):
st = scaling_function(time)
logp = keras.ops.zeros((), dtype=z.dtype)
for c in constraints:
ck = c(z)
logp = logp - keras.ops.softplus(st * ck)
return keras.ops.sum(logp) if reduce == "sum" else keras.ops.mean(logp)
backend = keras.backend.backend()
match backend:
case "jax":
import jax
grad = jax.grad(objective_fn)(x)
case "tensorflow":
import tensorflow as tf
with tf.GradientTape() as tape:
tape.watch(x)
objective = objective_fn(x)
grad = tape.gradient(objective, x)
case "torch":
import torch
with torch.enable_grad():
x_grad = x.clone().detach().requires_grad_(True)
objective = objective_fn(x_grad)
grad = torch.autograd.grad(
outputs=objective,
inputs=x_grad,
)[0]
case _:
raise NotImplementedError(f"Unsupported backend: {backend}")
return guidance_strength * grad
[docs]
def convert_prediction_to_x(
self, pred: Tensor, z: Tensor, alpha_t: Tensor, sigma_t: Tensor, log_snr_t: Tensor, prediction_type: str
) -> Tensor:
"""
Converts the neural network prediction into the denoised data `x`, depending on
the prediction type configured for the model.
Parameters
----------
pred : Tensor
The output prediction from the neural network, typically representing noise,
velocity, or a transformation of the clean signal.
z : Tensor
The noisy latent variable `z` to be denoised.
alpha_t : Tensor
The noise schedule's scaling factor for the clean signal at time `t`.
sigma_t : Tensor
The standard deviation of the noise at time `t`.
log_snr_t : Tensor
The log signal-to-noise ratio at time `t`.
prediction_type : str
The type of prediction made by the model, which determines how to convert it to `x`.
Must be one of {'velocity', 'noise', 'F', 'x', 'score'}.
Returns
-------
Tensor
The reconstructed clean signal `x` from the model prediction.
"""
match prediction_type:
case "velocity":
return alpha_t * z - sigma_t * pred
case "noise":
return (z - sigma_t * pred) / alpha_t
case "F":
sigma_data = getattr(self.noise_schedule, "sigma_data", 1.0)
x1 = (sigma_data**2 * alpha_t) / (ops.exp(-log_snr_t) + sigma_data**2)
x2 = ops.exp(-log_snr_t / 2) * sigma_data / ops.sqrt(ops.exp(-log_snr_t) + sigma_data**2)
return x1 * z + x2 * pred
case "x":
return pred
case "score":
return (z + sigma_t**2 * pred) / alpha_t
case "potential":
# Score is computed as ∇_z phi via _compute_grad_of_potential.
raise RuntimeError("convert_prediction_to_x should not be called for prediction_type='potential'. ")
case _:
raise ValueError(f"Unknown prediction type {prediction_type}.")
[docs]
def score(
self,
xz: Tensor,
time: float | Tensor = None,
log_snr_t: Tensor = None,
conditions: Tensor = None,
training: bool = False,
guidance_constraints: Mapping[str, Any] = None,
guidance_function: Callable[[Tensor, Tensor], Tensor] = None,
**kwargs,
) -> Tensor:
"""
Computes the score of the target or latent variable `xz`.
Parameters
----------
xz : Tensor
The current state of the latent variable `z`, typically of shape (..., D),
where D is the dimensionality of the latent space.
time : float or Tensor
Scalar or tensor representing the time (or noise level) at which the velocity
should be computed. Will be broadcasted to xz. If None, log_snr_t must be provided.
log_snr_t : Tensor
The log signal-to-noise ratio at time `t`. If None, time must be provided.
conditions : Tensor, optional
Conditional inputs to the network, such as conditioning variables
or encoder outputs. Shape must be broadcastable with `xz`. Default is None.
training : bool, optional
Whether the model is in training mode. Affects behavior of dropout, batch norm,
or other stochastic layers. Default is False.
guidance_constraints : dict[str, Any], optional
A dictionary of parameters for computing a guidance constraint term, which is
added to the score for guided sampling. The specific keys and values depend on
the implementation of `guidance_constraint_term`.
guidance_function : Callable[[Tensor, Tensor], Tensor], optional
A custom function for computing a guidance term, which is added to the score
for guided sampling. The function should accept the predicted clean signal
`x_pred` and the current time `time` as inputs and return a tensor of the same
shape as `xz`.
**kwargs
Subnet kwargs (e.g., attention_mask, mask) for the subnet layer.
Also supports guidance_constraints and guidance_function for custom guidance.
Returns
-------
Tensor
The velocity tensor of the same shape as `xz`, representing the right-hand
side of the probability-flow SDE or ODE at the given `time`.
"""
subnet_kwargs = self._collect_mask_kwargs(self._SUBNET_MASK_KEYS, kwargs)
if log_snr_t is None:
log_snr_t = self.noise_schedule.get_log_snr(t=time, training=training)
log_snr_t = expand_right_as(log_snr_t, xz)
log_snr_t = ops.broadcast_to(log_snr_t, ops.shape(xz)[:-1] + (1,))
if time is None:
time = self.noise_schedule.get_t_from_log_snr(log_snr_t, training=training)
alpha_t, sigma_t = self.noise_schedule.get_alpha_sigma(log_snr_t=log_snr_t)
norm_log_snr = self._transform_log_snr(log_snr_t)
if self._prediction_type == "potential":
pred = self._compute_grad_of_potential(
xz=xz, norm_log_snr=norm_log_snr, conditions=conditions, training=training, **subnet_kwargs
)
x_pred = self.convert_prediction_to_x(
pred=pred, z=xz, alpha_t=alpha_t, sigma_t=sigma_t, log_snr_t=log_snr_t, prediction_type="velocity"
)
else:
subnet_out = self.subnet((xz, norm_log_snr, conditions), training=training, **subnet_kwargs)
pred = self.output_projector(subnet_out)
x_pred = self.convert_prediction_to_x(
pred=pred,
z=xz,
alpha_t=alpha_t,
sigma_t=sigma_t,
log_snr_t=log_snr_t,
prediction_type=self._prediction_type,
)
score = (alpha_t * x_pred - xz) / ops.square(sigma_t)
if guidance_constraints is not None:
guidance = self.guidance_constraint_term(x=x_pred, time=time, **guidance_constraints)
score = score + guidance
if guidance_function is not None:
guidance = guidance_function(x=x_pred, time=time)
score = score + guidance
return score
[docs]
def velocity(
self,
xz: Tensor,
time: float | Tensor,
stochastic_solver: bool,
conditions: Tensor = None,
training: bool = False,
**kwargs,
) -> Tensor:
"""
Computes the velocity (i.e., time derivative) of the target or latent variable `xz` for either
a stochastic differential equation (SDE) or ordinary differential equation (ODE).
Parameters
----------
xz : Tensor
The current state of the latent variable `z`, typically of shape (..., D),
where D is the dimensionality of the latent space.
time : float or Tensor
Scalar or tensor representing the time (or noise level) at which the velocity
should be computed. Will be broadcasted to xz.
stochastic_solver : bool
If True, computes the velocity for the stochastic formulation (SDE).
If False, uses the deterministic formulation (ODE).
conditions : Tensor, optional
Conditional inputs to the network, such as conditioning variables
or encoder outputs. Shape must be broadcastable with `xz`. Default is None.
training : bool, optional
Whether the model is in training mode. Affects behavior of dropout, batch norm,
or other stochastic layers. Default is False.
Returns
-------
Tensor
The velocity tensor of the same shape as `xz`, representing the right-hand
side of the SDE or ODE at the given `time`.
"""
log_snr_t = expand_right_as(self.noise_schedule.get_log_snr(t=time, training=training), xz)
log_snr_t = ops.broadcast_to(log_snr_t, ops.shape(xz)[:-1] + (1,))
score = self.score(xz, log_snr_t=log_snr_t, conditions=conditions, training=training, **kwargs)
# compute velocity f, g of the SDE or ODE
f, g_squared = self.noise_schedule.get_drift(log_snr_t=log_snr_t, x=xz, training=training)
if stochastic_solver:
# for the SDE: d(z) = [f(z, t) - g(t) ^ 2 * score(z, lambda )] dt + g(t) dW
out = f - g_squared * score
else:
# for the ODE: d(z) = [f(z, t) - 0.5 * g(t) ^ 2 * score(z, lambda )] dt
out = f - 0.5 * g_squared * score
# Zero out velocity where target is fixed (during inference only)
if not training:
target_mask = kwargs.get("target_mask", None)
out = maybe_mask_tensor(out, mask=target_mask)
return out
[docs]
def diffusion_term(
self,
xz: Tensor,
time: float | Tensor,
training: bool = False,
**kwargs,
) -> Tensor:
"""
Compute the diffusion term (standard deviation of the noise) at a given time.
Parameters
----------
xz : Tensor
Input tensor of shape (..., D), typically representing the target or latent variables at given time.
time : float or Tensor
The diffusion time step(s). Can be a scalar or a tensor broadcastable to the shape of `xz`.
training : bool, optional
Whether to use the training noise schedule (default is False).
Returns
-------
Tensor
The diffusion term tensor with shape matching `xz` except for the last dimension, which is set to 1.
"""
log_snr_t = expand_right_as(self.noise_schedule.get_log_snr(t=time, training=training), xz)
log_snr_t = ops.broadcast_to(log_snr_t, ops.shape(xz)[:-1] + (1,))
g_squared = self.noise_schedule.get_drift(log_snr_t=log_snr_t)
g = ops.sqrt(g_squared)
# Zero out diffusion where target is fixed (during inference only)
if not training:
target_mask = kwargs.get("target_mask", None)
g = maybe_mask_tensor(g, mask=target_mask)
return g
def _velocity_trace(
self,
xz: Tensor,
time: Tensor,
conditions: Tensor = None,
max_steps: int = None,
training: bool = False,
**kwargs,
) -> tuple[Tensor, Tensor]:
def f(x):
return self.velocity(
x, time=time, stochastic_solver=False, conditions=conditions, training=training, **kwargs
)
v, trace = jacobian_trace(f, xz, max_steps=max_steps, seed=self.seed_generator, return_output=True)
return v, ops.expand_dims(trace, axis=-1)
def _compute_grad_of_potential(
self,
xz: Tensor,
norm_log_snr: Tensor,
conditions: Tensor = None,
training: bool = False,
**subnet_kwargs,
) -> Tensor:
"""
Compute the gradient of the predicted potential phi w.r.t. xz.
The network outputs a scalar potential phi(z, t, cond) per sample. The output is
then defined as ∇_z phi, i.e. the gradient of the potential w.r.t. the noisy input.
Parameters
----------
xz : Tensor
The noisy latent variable z at which to evaluate the score.
norm_log_snr : Tensor
Normalised log-SNR fed to the subnet as the time embedding.
conditions : Tensor, optional
Conditioning variables passed to the subnet. Default is None.
training : bool, optional
Whether the subnet is in training mode.
**subnet_kwargs
Additional keyword arguments forwarded to the subnet (e.g. attention masks).
Returns
-------
Tensor
Output of the same shape as *xz*, equal to some parameterization of ∇_xz phi(xz, t, cond).
"""
backend = keras.backend.backend()
match backend:
case "jax":
import jax
import jax.numpy as jnp
def phi_fn(x):
subnet_out = self.subnet(
(x, norm_log_snr, conditions),
training=training,
**subnet_kwargs,
)
return self.output_projector(subnet_out)
phi, vjp_fn = jax.vjp(phi_fn, xz)
out = vjp_fn(jnp.ones_like(phi))[0]
return out
case "tensorflow":
import tensorflow as tf
with tf.GradientTape() as tape:
tape.watch(xz)
subnet_out = self.subnet(
(xz, norm_log_snr, conditions),
training=training,
**subnet_kwargs,
)
phi = self.output_projector(subnet_out)
out = tape.gradient(
target=phi,
sources=xz,
output_gradients=tf.ones_like(phi),
)
return out
case "torch":
import torch
with torch.enable_grad():
xz_leaf = xz.requires_grad_(True)
subnet_out = self.subnet(
(xz_leaf, norm_log_snr, conditions),
training=training,
**subnet_kwargs,
)
phi = self.output_projector(subnet_out)
out = torch.autograd.grad(
outputs=phi,
inputs=xz_leaf,
grad_outputs=torch.ones_like(phi),
create_graph=training,
retain_graph=training,
)[0]
return out
case _:
raise NotImplementedError(f"Unsupported backend for potential prediction type: {backend}")
def _transform_log_snr(self, log_snr: Tensor) -> Tensor:
"""Transform the log_snr to the range [-1, 1] for the diffusion process."""
log_snr_min = self.noise_schedule.log_snr_min
log_snr_max = self.noise_schedule.log_snr_max
normalized_snr = (log_snr - log_snr_min) / (log_snr_max - log_snr_min)
scaled_value = 2 * normalized_snr - 1
return scaled_value
def _forward(
self,
x: Tensor,
conditions: Tensor = None,
density: bool = False,
training: bool = False,
**kwargs,
) -> Tensor | tuple[Tensor, Tensor]:
# Note: integrators will cherry-pick necessary kwargs, so
# we can be general (i.e., sloppy) here
integrate_kwargs = {"start_time": 0.0, "stop_time": 1.0}
integrate_kwargs |= self.integrate_kwargs
integrate_kwargs |= kwargs
if integrate_kwargs["method"] in STOCHASTIC_METHODS:
logging.warning(
"Stochastic methods are not supported for density evaluation."
" Falling back to tsit5 ODE solver."
" To suppress this warning, explicitly pass a method from " + str(DETERMINISTIC_METHODS) + "."
)
integrate_kwargs["method"] = "tsit5"
# Apply user-provided target mask if available
target_mask = kwargs.get("target_mask", None)
targets_fixed = kwargs.get("targets_fixed", None)
if target_mask is not None:
target_mask = keras.ops.broadcast_to(target_mask, keras.ops.shape(x))
targets_fixed = keras.ops.broadcast_to(targets_fixed, keras.ops.shape(x))
x = maybe_mask_tensor(x, target_mask, replacement=targets_fixed)
if self.unconditional_mode and conditions is not None:
conditions = keras.ops.zeros_like(conditions)
logging.info("Condition masking is applied: conditions are set to zero.")
if density:
def deltas(time, xz):
v, trace = self._velocity_trace(xz, time=time, conditions=conditions, training=training, **kwargs)
return {"xz": v, "trace": trace}
state = {
"xz": x,
"trace": ops.zeros(ops.shape(x)[:-1] + (1,), dtype=ops.dtype(x)),
}
state = integrate(deltas, state, **integrate_kwargs)
z = state["xz"]
log_density = self.base_distribution.log_prob(z) + ops.squeeze(state["trace"], axis=-1)
return z, log_density
def deltas(time, xz):
return {
"xz": self.velocity(
xz, time=time, stochastic_solver=False, conditions=conditions, training=training, **kwargs
)
}
state = {"xz": x}
state = integrate(deltas, state, **integrate_kwargs)
z = state["xz"]
return z
def _inverse(
self, z: Tensor, conditions: Tensor = None, density: bool = False, training: bool = False, **kwargs
) -> Tensor | tuple[Tensor, Tensor]:
seed = resolve_seed(kwargs.pop("seed", None)) or self.seed_generator
# Build integrate kwargs: hardcoded defaults -> instance config -> call-time overrides
integrate_kwargs = {"start_time": 1.0, "stop_time": 0.0}
integrate_kwargs |= self.integrate_kwargs
integrate_kwargs |= kwargs
# Apply user-provided target mask if available
target_mask = kwargs.get("target_mask", None)
targets_fixed = kwargs.get("targets_fixed", None)
if target_mask is not None:
target_mask = keras.ops.broadcast_to(target_mask, keras.ops.shape(z))
targets_fixed = keras.ops.broadcast_to(targets_fixed, keras.ops.shape(z))
z = maybe_mask_tensor(z, target_mask, replacement=targets_fixed)
if self.unconditional_mode and conditions is not None:
conditions = keras.ops.zeros_like(conditions)
logging.info("Condition masking is applied: conditions are set to zero.")
if density:
if integrate_kwargs["method"] in STOCHASTIC_METHODS:
logging.warning(
"Stochastic methods are not supported for density computation."
" Falling back to ODE solver."
" Use one of the deterministic methods: " + str(DETERMINISTIC_METHODS) + "."
)
integrate_kwargs["method"] = "tsit5"
def deltas(time, xz):
v, trace = self._velocity_trace(xz, time=time, conditions=conditions, training=training, **kwargs)
return {"xz": v, "trace": trace}
state = {
"xz": z,
"trace": ops.zeros(ops.shape(z)[:-1] + (1,), dtype=ops.dtype(z)),
}
state = integrate(deltas, state, **integrate_kwargs)
x = state["xz"]
log_density = self.base_distribution.log_prob(z) - ops.squeeze(state["trace"], axis=-1)
return x, log_density
state = {"xz": z}
if integrate_kwargs["method"] in STOCHASTIC_METHODS:
def deltas(time, xz):
return {
"xz": self.velocity(
xz, time=time, stochastic_solver=True, conditions=conditions, training=training, **kwargs
)
}
def diffusion(time, xz):
return {"xz": self.diffusion_term(xz, time=time, training=training, **kwargs)}
score_fn = None
if "corrector_steps" in integrate_kwargs or integrate_kwargs["method"] == "langevin":
def score_fn(time, xz):
return {"xz": self.score(xz, time=time, conditions=conditions, training=training, **kwargs)}
state = integrate_stochastic(
drift_fn=deltas,
diffusion_fn=diffusion,
score_fn=score_fn,
noise_schedule=self.noise_schedule,
state=state,
seed=seed,
**integrate_kwargs,
)
else:
def deltas(time, xz):
return {
"xz": self.velocity(
xz, time=time, stochastic_solver=False, conditions=conditions, training=training, **kwargs
)
}
state = integrate(deltas, state, **integrate_kwargs)
x = state["xz"]
return x
[docs]
def compositional_bridge(self, time: Tensor) -> Tensor:
"""Bridge function for compositional diffusion. In the simplest case,
this is just 1 if d0 = d1 = 1. Otherwise, it can be used to stabilize the
compositional score over time.
Parameters
----------
time: Tensor
Time step for the diffusion process.
Returns
-------
Tensor
Bridge function value with same shape as time.
"""
return self.compositional_bridge_d0 * ops.exp(
-ops.log(self.compositional_bridge_d0 / self.compositional_bridge_d1) * time
)
[docs]
def compositional_velocity(
self,
xz: Tensor,
time: float | Tensor,
stochastic_solver: bool,
conditions: Tensor,
seed: keras.random.SeedGenerator,
compute_prior_score: Callable[[Tensor], Tensor] = None,
mini_batch_size: int | None = None,
training: bool = False,
**kwargs,
) -> Tensor:
"""
Computes the compositional velocity for multiple datasets using the formula:
s_ψ(θ,t,Y) = (1-n)(1-t) ∇_θ log p(θ) + Σᵢ₌₁ⁿ s_ψ(θ,t,yᵢ)
Parameters
----------
xz : Tensor
The current state of the latent variable, shape (num_datasets, num_items, ...)
time : float or Tensor
Time step for the diffusion process
stochastic_solver : bool
Whether to use stochastic (SDE) or deterministic (ODE) formulation
conditions : Tensor
Conditional inputs with compositional structure (num_datasets, num_items, ...)
seed: SeedGenerator
For reproducibility.
compute_prior_score: Callable, optional
Function to compute the prior score ∇_θ log p(θ). Otherwise, the unconditional
score is used.
mini_batch_size : int or None
Mini batch size for computing individual scores. If None, use all conditions.
training : bool, optional
Whether in training mode
**kwargs
Additional keyword arguments passed to the individual score computation.
Returns
-------
Tensor
Compositional velocity of same shape as input xz
"""
compositional_score = self.compositional_score(
xz=xz,
time=time,
conditions=conditions,
compute_prior_score=compute_prior_score,
mini_batch_size=mini_batch_size,
training=training,
seed=seed,
**kwargs,
)
# Calculate standard noise schedule components
log_snr_t = expand_right_as(self.noise_schedule.get_log_snr(t=time, training=training), xz)
log_snr_t = ops.broadcast_to(log_snr_t, ops.shape(xz)[:-1] + (1,))
# Compute velocity using standard drift-diffusion formulation
f, g_squared = self.noise_schedule.get_drift(log_snr_t=log_snr_t, x=xz, training=training)
if stochastic_solver:
# for the SDE: d(z) = [f(z, t) - g(t) ^ 2 * score(z, lambda )] dt + g(t) dW
out = f - g_squared * compositional_score
else:
# for the ODE: d(z) = [f(z, t) - 0.5 * g(t) ^ 2 * score(z, lambda )] dt
out = f - 0.5 * g_squared * compositional_score
# Zero out velocity where target is fixed (during inference only)
if not training:
target_mask = kwargs.get("target_mask", None)
out = maybe_mask_tensor(out, mask=target_mask)
return out
[docs]
def compositional_score(
self,
xz: Tensor,
time: float | Tensor,
conditions: Tensor,
seed: keras.random.SeedGenerator | None,
compute_prior_score: Callable[[Tensor], Tensor] = None,
mini_batch_size: int | None = None,
training: bool = False,
clip: tuple[float, float] | None = (-3, 3),
use_jac: bool = False,
guidance_constraints: Mapping[str, Any] = None,
guidance_function: Callable[[Tensor, Tensor], Tensor] = None,
**kwargs,
) -> Tensor:
"""
Computes the compositional score for multiple datasets.
Parameters
----------
xz : Tensor
The current state of the latent variable, shape (num_datasets, num_items, ...)
time : float or Tensor
Time step for the diffusion process
conditions : Tensor
Conditional inputs with compositional structure (num_datasets, num_items, ...)
seed: keras.random.SeedGenerator or None
Optional seed for reproducibility.
compute_prior_score: Callable, optional
Function to compute the prior score ∇_θ log p(θ). Otherwise, the unconditional score is used.
mini_batch_size : int or None
Mini batch size for computing individual scores. If None, use all conditions.
training : bool, optional
Whether in training mode
clip: (float, float), optional
Whether to clip the predicted x for numerical stability at given values.
use_jac: bool, optional
Whether to use the Jacobian-based compositional score instead of the direct sum.
guidance_constraints : dict[str, Any], optional
A dictionary of parameters for computing a guidance constraint term, which is
added to the score for guided sampling. The specific keys and values depend on
the implementation of `guidance_constraint_term`.
guidance_function : Callable[[Tensor, Tensor], Tensor], optional
A custom function for computing a guidance term, which is added to the score
for guided sampling. The function should accept the predicted clean signal
`x_pred` and the current time `time` as inputs and return a tensor of the same
shape as `xz`.
**kwargs
Additional keyword arguments passed to the individual score computation
Returns
-------
Tensor
Compositional velocity of same shape as input xz
"""
if conditions is None:
raise ValueError("Conditions are required for compositional sampling")
log_snr_t = expand_right_as(self.noise_schedule.get_log_snr(t=time, training=training), xz)
log_snr_t = ops.broadcast_to(log_snr_t, ops.shape(xz)[:-1] + (1,))
alpha_t, sigma_t = self.noise_schedule.get_alpha_sigma(log_snr_t=log_snr_t)
time = ops.cast(time, dtype=ops.dtype(xz))
if not use_jac:
compositional_score = self._compositional_score_direct(
xz=xz,
time=time,
log_snr_t=log_snr_t,
conditions=conditions,
compute_prior_score=compute_prior_score,
mini_batch_size=mini_batch_size,
training=training,
seed=seed,
**kwargs,
)
else:
# uses a Gaussian approximation, can be very slow
compositional_score = self._compositional_score_jac(
xz=xz,
time=time,
log_snr_t=log_snr_t,
sigma_t=sigma_t,
conditions=conditions,
compute_prior_score=compute_prior_score,
mini_batch_size=mini_batch_size,
training=training,
seed=seed,
**kwargs,
)
compositional_score = self.compositional_bridge(time) * compositional_score
if guidance_constraints is not None or guidance_function is not None:
# x_pred = (z + sigma_t ** 2 * score) / alpha_t
x_pred = (xz + sigma_t**2 * compositional_score) / alpha_t
if guidance_constraints is not None:
guidance = self.guidance_constraint_term(x=x_pred, time=time, **guidance_constraints)
compositional_score = compositional_score + guidance
if guidance_function is not None:
guidance = guidance_function(x=x_pred, time=time)
compositional_score = compositional_score + guidance
compositional_score = self._maybe_clip_score(compositional_score, clip, alpha_t, sigma_t, xz)
return compositional_score
def _compositional_score_direct(
self,
xz: Tensor,
time: float | Tensor,
log_snr_t: Tensor,
conditions: Tensor,
seed: keras.random.SeedGenerator | None = None,
compute_prior_score: Callable[[Tensor], Tensor] = None,
mini_batch_size: int | None = None,
training: bool = False,
**kwargs,
) -> Tensor:
"""
Computes the compositional score for multiple datasets using the formula:
s_ψ(θ,t,Y) = (1-n)(1-t) ∇_θ log p(θ) + Σᵢ₌₁ⁿ s_ψ(θ,t,yᵢ)
with possible weighting of the scores.
Parameters
----------
xz : Tensor
The current state of the latent variable, shape (num_datasets, num_items, ...)
time : float or Tensor
Time step for the diffusion process.
log_snr_t : Tensor
Log SNR at time t, broadcastable to shape of xz.
conditions : Tensor
Conditional inputs with compositional structure (num_datasets, num_items, ...)
seed: keras.random.SeedGenerator or None
Optional seed for reproducibility.
compute_prior_score: Callable, optional
Function to compute the prior score ∇_θ log p(θ). Otherwise, the unconditional score is estimated.
mini_batch_size : int or None
Mini batch size for computing individual scores. If None, use all conditions.
training : bool, optional
Whether in training mode.
**kwargs
Additional keyword arguments passed to the individual score computation.
Returns
-------
Tensor
Compositional score of same shape as input xz
"""
batch_size, num_items = ops.shape(conditions)[:2]
# Sample item indices for mini-batching or keep all items
if mini_batch_size is not None and mini_batch_size < num_items:
ranks = keras.random.uniform((batch_size, num_items), seed=seed)
per_row_idx = ops.top_k(-ranks, mini_batch_size).indices
conditions_batch = ops.take_along_axis(conditions, per_row_idx[..., None], axis=1)
else:
conditions_batch = conditions
mini_batch_size = num_items
# Determine scale of summed posterior score
needs_network_prior = compute_prior_score is None
if needs_network_prior:
zero_cond = ops.zeros_like(ops.take(conditions, 0, axis=1))
cond_with_prior = ops.concatenate([conditions_batch, ops.expand_dims(zero_cond, 1)], axis=1)
num_total = mini_batch_size + 1
else:
cond_with_prior = conditions_batch
num_total = mini_batch_size
scale = num_items / mini_batch_size
# Expand and flatten compositional dimension (i.e., num items) for score computation
dims = tuple(ops.shape(xz)[1:])
snr_dims = tuple(ops.shape(log_snr_t)[1:])
conditions_dims = tuple(ops.shape(cond_with_prior)[2:])
xz_reshaped = ops.reshape(
ops.repeat(ops.expand_dims(xz, 1), num_total, axis=1), (batch_size * num_total,) + dims
)
log_snr_reshaped = ops.reshape(
ops.repeat(ops.expand_dims(log_snr_t, 1), num_total, axis=1),
(batch_size * num_total,) + snr_dims,
)
conditions_flat = ops.reshape(cond_with_prior, (batch_size * num_total,) + conditions_dims)
scores_flat = self.score(
xz_reshaped,
log_snr_t=log_snr_reshaped,
conditions=conditions_flat,
training=training,
**kwargs,
)
all_scores = ops.reshape(scores_flat, (batch_size, num_total) + dims)
individual_scores = all_scores[:, :mini_batch_size]
if needs_network_prior:
prior_score = all_scores[:, -1]
else:
# internally uses a (1-time) weight if prior score has no time argument
prior_score = compute_prior_score(xz, time)
# Combined score using compositional formula: (1-n) prior_score + Σᵢ₌₁ⁿ posterior_score
delta = individual_scores - ops.expand_dims(prior_score, axis=1)
update_delta = scale * ops.sum(delta, axis=1)
compositional_score = prior_score + update_delta
return compositional_score
def _compositional_score_jac(
self,
xz: Tensor,
time: float | Tensor,
log_snr_t: Tensor,
sigma_t: Tensor,
conditions: Tensor,
seed: keras.random.SeedGenerator | None = None,
compute_prior_score: Callable[[Tensor], Tensor] | None = None,
mini_batch_size: int | None = None,
training: bool = False,
regularize_precision: float = 1e-6,
**kwargs,
) -> Tensor:
"""Stabilized version of JAC compositional score (Linhart et al. 2026) with mini-batching from
(Arruda et al. 2026).
Precision-weighted compositional posterior score where both individual posterior precisions
and the prior precision are estimated via the Jacobian of the score network.
Parameters
----------
xz : Tensor
The current state of the latent variable, shape (num_datasets, num_items, ...)
time : float or Tensor
Time step for the diffusion process.
log_snr_t : Tensor
Log SNR at time t, broadcastable to shape of xz.
sigma_t : Tensor
Sigma component of noise schedule at time t, broadcastable to shape of xz.
conditions : Tensor
Conditional inputs with compositional structure (num_datasets, num_items, ...)
seed: SeedGenerator or None
Optional seed for reproducibility.
compute_prior_score: Callable, optional
Function to compute the prior score ∇_θ log p(θ). Otherwise, the unconditional score is used.
mini_batch_size : int or None, optional
Mini batch size for computing individual scores. If None, use all conditions.
training : bool
Whether in training mode.
regularize_precision : float
Tikhonov regularization added to Λ before solving for numerical stability.
**kwargs
Additional keyword arguments passed to the individual score computation.
Returns
-------
Tensor
Compositional score of same shape as input xz
"""
batch_size, num_items = ops.shape(conditions)[:2]
m = ops.shape(xz)[-1]
upsilon_t = ops.maximum(ops.reshape(sigma_t, (-1,))[0] ** 2, 1e-8)
if mini_batch_size is not None and mini_batch_size < num_items:
ranks = keras.random.uniform((batch_size, num_items), seed=seed)
per_row_idx = ops.top_k(-ranks, mini_batch_size).indices
conditions_batch = ops.take_along_axis(conditions, per_row_idx[..., None], axis=1)
else:
conditions_batch = conditions
mini_batch_size = num_items
# Append prior as extra observation (zero-conditioned)
zero_cond = ops.zeros_like(ops.take(conditions, 0, axis=1))
cond_with_prior = ops.concatenate([conditions_batch, ops.expand_dims(zero_cond, 1)], axis=1)
num_total = mini_batch_size + 1
dims = tuple(ops.shape(xz)[1:])
snr_dims = tuple(ops.shape(log_snr_t)[1:])
cond_dims = tuple(ops.shape(cond_with_prior)[2:])
# Repeat xz and log_snr_t for each observation+prior
xz_rep = ops.reshape(
ops.repeat(ops.expand_dims(xz, 1), num_total, axis=1),
(batch_size * num_total,) + dims,
)
lsnr_rep = ops.reshape(
ops.repeat(ops.expand_dims(log_snr_t, 1), num_total, axis=1),
(batch_size * num_total,) + snr_dims,
)
cond_flat = ops.reshape(
cond_with_prior,
(batch_size * num_total,) + cond_dims,
)
all_scores, all_jacs = self._compute_score_and_jacobian(
xz=xz_rep,
log_snr_t=lsnr_rep,
conditions=cond_flat,
training=training,
**kwargs,
)
# Reshape: (B, num_total, m) and (B, num_total, m, m)
all_scores = ops.reshape(all_scores, (batch_size, num_total, m))
all_jacs = ops.reshape(all_jacs, (batch_size, num_total, m, m))
# compute P_k = (I + υ J_k)⁻¹ for all k at once
I_m = ops.eye(m, dtype=ops.dtype(xz))
I_4d = ops.broadcast_to(
ops.reshape(I_m, (1, 1, m, m)),
(batch_size, num_total, m, m),
)
A_all = I_4d + upsilon_t * all_jacs
P_all = ops.inv(A_all)
# P_k @ s_k for all k: (B, num_total, m, 1) → (B, num_total, m)
scores_col = ops.expand_dims(all_scores, -1)
Ps_all = ops.squeeze(ops.matmul(P_all, scores_col), axis=-1) # (B, num_total, m)
# split observations and prior
P_obs = P_all[:, :mini_batch_size] # (B, n_obs, m, m)
Ps_obs = Ps_all[:, :mini_batch_size] # (B, n_obs, m)
P_lambda = P_all[:, -1] # (B, m, m)
# Sum over observations
sum_P = ops.sum(P_obs, axis=1) # (B, m, m)
sum_Ps = ops.sum(Ps_obs, axis=1) # (B, m)
# Scale for mini-batch estimator
if mini_batch_size < num_items:
scale = num_items / mini_batch_size
sum_P = scale * sum_P
sum_Ps = scale * sum_Ps
# prior score
if compute_prior_score is not None:
s_lambda = compute_prior_score(xz, time)
P_lambda_s = ops.squeeze(ops.matmul(P_lambda, ops.expand_dims(s_lambda, -1)), axis=-1)
else:
P_lambda_s = Ps_all[:, -1] # already computed
# solve: Λ x = s̃
w_prior = 1 - num_items
I_m_batch = ops.broadcast_to(I_m, (batch_size, m, m))
lambda_matrix = sum_P + w_prior * P_lambda + regularize_precision * I_m_batch
s_tilde = sum_Ps + w_prior * P_lambda_s
compositional_score = linsolve_batched(lambda_matrix, s_tilde)
return compositional_score
def _compute_score_and_jacobian(
self,
xz: Tensor,
log_snr_t: Tensor,
conditions: Tensor,
training: bool = False,
**kwargs,
) -> tuple[Tensor, Tensor]:
"""Compute score and JAC precision Σ̂⁻¹ for one conditioning input using full Jacobian J = ∇_{θ_t} s(θ_t).
Returns
-------
s : Tensor (B, m)
prec : Tensor (B, m, m)
Σ̂⁻¹ = (α_t/υ_t)(I + υ_t J)⁻¹
"""
m = ops.shape(xz)[-1]
backend = keras.backend.backend()
match backend:
case "jax":
import jax
import jax.numpy as jnp
def phi_fn(x):
return self.score(
xz=x,
log_snr_t=log_snr_t,
conditions=conditions,
training=training,
**kwargs,
)
score, vjp_fn = jax.vjp(phi_fn, xz)
rows = []
for i in range(m):
e_i = jnp.zeros_like(score).at[:, i].set(1.0)
(row_i,) = vjp_fn(e_i)
rows.append(jnp.expand_dims(row_i, axis=1))
jacobian = jnp.concatenate(rows, axis=1)
case "tensorflow":
import tensorflow as tf
with tf.GradientTape(persistent=True) as tape:
tape.watch(xz)
score = self.score(
xz=xz,
log_snr_t=log_snr_t,
conditions=conditions,
training=training,
**kwargs,
)
if m <= 32: # for larger dimension
rows = []
for i in range(m):
e_i = tf.one_hot(tf.fill([tf.shape(score)[0]], i), depth=m, dtype=score.dtype)
row_i = tape.gradient(score, xz, output_gradients=e_i)
rows.append(tf.expand_dims(row_i, axis=1))
jacobian = tf.concat(rows, axis=1)
else:
jacobian = tape.batch_jacobian(score, xz, experimental_use_pfor=False)
del tape
case "torch":
import torch
with torch.enable_grad():
xz_leaf = xz.detach().requires_grad_(True)
score = self.score(
xz=xz_leaf,
log_snr_t=log_snr_t,
conditions=conditions,
training=training,
**kwargs,
)
rows = []
for i in range(m):
e_i = torch.zeros_like(score)
e_i[:, i] = 1.0
(row_i,) = torch.autograd.grad(
outputs=score,
inputs=xz_leaf,
grad_outputs=e_i,
create_graph=False,
retain_graph=(i < m - 1),
)
rows.append(row_i.unsqueeze(1))
jacobian = torch.cat(rows, dim=1)
score = score.detach()
case _:
raise NotImplementedError(f"JAC Jacobian not implemented for backend '{backend}'. ")
return score, jacobian
@staticmethod
def _maybe_clip_score(compositional_score, clip, alpha_t, sigma_t, xz):
if clip is not None:
min_clip, max_clip = clip
x_pred = (xz + sigma_t**2 * compositional_score) / alpha_t
x_pred = ops.clip(x_pred, min_clip, max_clip)
compositional_score = (x_pred * alpha_t - xz) / (sigma_t**2)
return compositional_score
def _inverse_compositional(
self,
z: Tensor,
conditions: Tensor,
compute_prior_score: Callable[[Tensor], Tensor] = None,
density: bool = False,
training: bool = False,
**kwargs,
) -> Tensor | tuple[Tensor, Tensor]:
"""
Inverse pass for compositional diffusion sampling.
"""
seed = resolve_seed(kwargs.pop("seed", None)) or self.seed_generator
integrate_kwargs = {"start_time": 1.0, "stop_time": 0.0}
integrate_kwargs |= self.integrate_kwargs
integrate_kwargs |= kwargs
num_items = ops.shape(conditions)[1]
mini_batch_size = int(integrate_kwargs.pop("mini_batch_size", max(num_items * 0.1, 2)))
if "mini_batch_size" in kwargs:
kwargs.pop("mini_batch_size")
if mini_batch_size is None:
mini_batch_size = num_items
mini_batch_size = max(mini_batch_size, 1)
if keras.backend.backend() == "jax" and mini_batch_size != num_items:
mini_batch_size = num_items
logging.warning("Setting mini_batch_size to num_items as jax does not support mini-batching.")
self.compositional_bridge_d0 = float(
integrate_kwargs.pop("compositional_bridge_d0", self.compositional_bridge_d0)
)
self.compositional_bridge_d1 = float(
integrate_kwargs.pop("compositional_bridge_d1", self.compositional_bridge_d1)
)
if integrate_kwargs["method"] == "langevin": # Geffner et al. (2023)
z_scaling = num_items * self.compositional_bridge_d1
z = z / ops.sqrt(ops.cast(z_scaling, dtype=ops.dtype(z)))
# Apply user-provided target mask if available
target_mask = kwargs.get("target_mask", None)
targets_fixed = kwargs.get("targets_fixed", None)
if target_mask is not None:
target_mask = keras.ops.broadcast_to(target_mask, keras.ops.shape(z))
targets_fixed = keras.ops.broadcast_to(targets_fixed, keras.ops.shape(z))
z = maybe_mask_tensor(z, target_mask, replacement=targets_fixed)
if density:
if integrate_kwargs["method"] in STOCHASTIC_METHODS:
logging.warning(
"Stochastic methods are not supported for density computation."
" Falling back to ODE solver."
" Use one of the deterministic methods: " + str(DETERMINISTIC_METHODS) + "."
)
integrate_kwargs["method"] = "tsit5"
def deltas(time, xz):
v = self.compositional_velocity(
xz,
time=time,
stochastic_solver=False,
conditions=conditions,
compute_prior_score=compute_prior_score,
mini_batch_size=mini_batch_size,
training=training,
seed=seed,
**kwargs,
)
trace = ops.zeros(ops.shape(xz)[:-1] + (1,), dtype=ops.dtype(xz))
return {"xz": v, "trace": trace}
state = {
"xz": z,
"trace": ops.zeros(ops.shape(z)[:-1] + (1,), dtype=ops.dtype(z)),
}
state = integrate(deltas, state, **integrate_kwargs)
x = state["xz"]
log_density = self.base_distribution.log_prob(z) - ops.squeeze(state["trace"], axis=-1)
return x, log_density
state = {"xz": z}
if integrate_kwargs["method"] in STOCHASTIC_METHODS:
def deltas(time, xz):
return {
"xz": self.compositional_velocity(
xz,
time=time,
stochastic_solver=True,
conditions=conditions,
compute_prior_score=compute_prior_score,
mini_batch_size=mini_batch_size,
training=training,
seed=seed,
**kwargs,
)
}
def diffusion(time, xz):
return {"xz": self.diffusion_term(xz, time=time, training=training, **kwargs)}
score_fn = None
if "corrector_steps" in integrate_kwargs or integrate_kwargs["method"] == "langevin":
def score_fn(time, xz):
return {
"xz": self.compositional_score(
xz=xz,
time=time,
conditions=conditions,
compute_prior_score=compute_prior_score,
mini_batch_size=mini_batch_size,
training=training,
seed=seed,
**kwargs,
)
}
state = integrate_stochastic(
drift_fn=deltas,
diffusion_fn=diffusion,
score_fn=score_fn,
noise_schedule=self.noise_schedule,
state=state,
seed=seed,
**integrate_kwargs,
)
else:
def deltas(time, xz):
return {
"xz": self.compositional_velocity(
xz,
time=time,
stochastic_solver=False,
conditions=conditions,
compute_prior_score=compute_prior_score,
mini_batch_size=mini_batch_size,
training=training,
seed=seed,
**kwargs,
)
}
state = integrate(deltas, state, **integrate_kwargs)
x = state["xz"]
return x
