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transport/__init__.py

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+from .transport import Transport, ModelType, WeightType, PathType, SNRType, Sampler
+
+
+def create_transport(
+    path_type="Linear",
+    prediction="velocity",
+    loss_weight=None,
+    train_eps=None,
+    sample_eps=None,
+    snr_type="uniform",
+):
+    """function for creating Transport object
+    **Note**: model prediction defaults to velocity
+    Args:
+    - path_type: type of path to use; default to linear
+    - learn_score: set model prediction to score
+    - learn_noise: set model prediction to noise
+    - velocity_weighted: weight loss by velocity weight
+    - likelihood_weighted: weight loss by likelihood weight
+    - train_eps: small epsilon for avoiding instability during training
+    - sample_eps: small epsilon for avoiding instability during sampling
+    """
+
+    if prediction == "noise":
+        model_type = ModelType.NOISE
+    elif prediction == "score":
+        model_type = ModelType.SCORE
+    else:
+        model_type = ModelType.VELOCITY
+
+    if loss_weight == "velocity":
+        loss_type = WeightType.VELOCITY
+    elif loss_weight == "likelihood":
+        loss_type = WeightType.LIKELIHOOD
+    else:
+        loss_type = WeightType.NONE
+
+    if snr_type == "lognorm":
+        snr_type = SNRType.LOGNORM
+    elif snr_type == "uniform":
+        snr_type = SNRType.UNIFORM
+    else:
+        raise ValueError(f"Invalid snr type {snr_type}")
+
+    path_choice = {
+        "Linear": PathType.LINEAR,
+        "GVP": PathType.GVP,
+        "VP": PathType.VP,
+    }
+
+    path_type = path_choice[path_type]
+
+    if path_type in [PathType.VP]:
+        train_eps = 1e-5 if train_eps is None else train_eps
+        sample_eps = 1e-3 if train_eps is None else sample_eps
+    elif (
+        path_type in [PathType.GVP, PathType.LINEAR]
+        and model_type != ModelType.VELOCITY
+    ):
+        train_eps = 1e-3 if train_eps is None else train_eps
+        sample_eps = 1e-3 if train_eps is None else sample_eps
+    else:  # velocity & [GVP, LINEAR] is stable everywhere
+        train_eps = 0
+        sample_eps = 0
+
+    # create flow state
+    state = Transport(
+        model_type=model_type,
+        path_type=path_type,
+        loss_type=loss_type,
+        train_eps=train_eps,
+        sample_eps=sample_eps,
+        snr_type=snr_type,
+    )
+
+    return state

transport/integrators.py

@@ -0,0 +1,127 @@
+import numpy as np
+import torch as th
+import torch.nn as nn
+from torchdiffeq import odeint
+from functools import partial
+from tqdm import tqdm
+
+
+class sde:
+    """SDE solver class"""
+
+    def __init__(
+        self,
+        drift,
+        diffusion,
+        *,
+        t0,
+        t1,
+        num_steps,
+        sampler_type,
+    ):
+        assert t0 < t1, "SDE sampler has to be in forward time"
+
+        self.num_timesteps = num_steps
+        self.t = th.linspace(t0, t1, num_steps)
+        self.dt = self.t[1] - self.t[0]
+        self.drift = drift
+        self.diffusion = diffusion
+        self.sampler_type = sampler_type
+
+    def __Euler_Maruyama_step(self, x, mean_x, t, model, **model_kwargs):
+        w_cur = th.randn(x.size()).to(x)
+        t = th.ones(x.size(0)).to(x) * t
+        dw = w_cur * th.sqrt(self.dt)
+        drift = self.drift(x, t, model, **model_kwargs)
+        diffusion = self.diffusion(x, t)
+        mean_x = x + drift * self.dt
+        x = mean_x + th.sqrt(2 * diffusion) * dw
+        return x, mean_x
+
+    def __Heun_step(self, x, _, t, model, **model_kwargs):
+        w_cur = th.randn(x.size()).to(x)
+        dw = w_cur * th.sqrt(self.dt)
+        t_cur = th.ones(x.size(0)).to(x) * t
+        diffusion = self.diffusion(x, t_cur)
+        xhat = x + th.sqrt(2 * diffusion) * dw
+        K1 = self.drift(xhat, t_cur, model, **model_kwargs)
+        xp = xhat + self.dt * K1
+        K2 = self.drift(xp, t_cur + self.dt, model, **model_kwargs)
+        return (
+            xhat + 0.5 * self.dt * (K1 + K2),
+            xhat,
+        )  # at last time point we do not perform the heun step
+
+    def __forward_fn(self):
+        """TODO: generalize here by adding all private functions ending with steps to it"""
+        sampler_dict = {
+            "Euler": self.__Euler_Maruyama_step,
+            "Heun": self.__Heun_step,
+        }
+
+        try:
+            sampler = sampler_dict[self.sampler_type]
+        except:
+            raise NotImplementedError("Smapler type not implemented.")
+
+        return sampler
+
+    def sample(self, init, model, **model_kwargs):
+        """forward loop of sde"""
+        x = init
+        mean_x = init
+        samples = []
+        sampler = self.__forward_fn()
+        for ti in self.t[:-1]:
+            with th.no_grad():
+                x, mean_x = sampler(x, mean_x, ti, model, **model_kwargs)
+                samples.append(x)
+
+        return samples
+
+
+class ode:
+    """ODE solver class"""
+
+    def __init__(
+        self,
+        drift,
+        *,
+        t0,
+        t1,
+        sampler_type,
+        num_steps,
+        atol,
+        rtol,
+        time_shifting_factor=None,
+    ):
+        assert t0 < t1, "ODE sampler has to be in forward time"
+
+        self.drift = drift
+        self.t = th.linspace(t0, t1, num_steps)
+        if time_shifting_factor:
+            self.t = self.t / (
+                self.t + time_shifting_factor - time_shifting_factor * self.t
+            )
+        self.atol = atol
+        self.rtol = rtol
+        self.sampler_type = sampler_type
+
+    def sample(self, x, model, **model_kwargs):
+
+        device = x[0].device if isinstance(x, tuple) else x.device
+
+        def _fn(t, x):
+            t = (
+                th.ones(x[0].size(0)).to(device) * t
+                if isinstance(x, tuple)
+                else th.ones(x.size(0)).to(device) * t
+            )
+            model_output = self.drift(x, t, model, **model_kwargs)
+            return model_output
+
+        t = self.t.to(device)
+        atol = [self.atol] * len(x) if isinstance(x, tuple) else [self.atol]
+        rtol = [self.rtol] * len(x) if isinstance(x, tuple) else [self.rtol]
+        samples = odeint(_fn, x, t, method=self.sampler_type, atol=atol, rtol=rtol)
+        return samples

transport/path.py

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+import torch as th
+import numpy as np
+from functools import partial
+
+
+def expand_t_like_x(t, x):
+    """Function to reshape time t to broadcastable dimension of x
+    Args:
+      t: [batch_dim,], time vector
+      x: [batch_dim,...], data point
+    """
+    dims = [1] * len(x[0].size())
+    t = t.view(t.size(0), *dims)
+    return t
+
+
+#################### Coupling Plans ####################
+
+
+class ICPlan:
+    """Linear Coupling Plan"""
+
+    def __init__(self, sigma=0.0):
+        self.sigma = sigma
+
+    def compute_alpha_t(self, t):
+        """Compute the data coefficient along the path"""
+        return t, 1
+
+    def compute_sigma_t(self, t):
+        """Compute the noise coefficient along the path"""
+        return 1 - t, -1
+
+    def compute_d_alpha_alpha_ratio_t(self, t):
+        """Compute the ratio between d_alpha and alpha"""
+        return 1 / t
+
+    def compute_drift(self, x, t):
+        """We always output sde according to score parametrization;"""
+        t = expand_t_like_x(t, x)
+        alpha_ratio = self.compute_d_alpha_alpha_ratio_t(t)
+        sigma_t, d_sigma_t = self.compute_sigma_t(t)
+        drift = alpha_ratio * x
+        diffusion = alpha_ratio * (sigma_t**2) - sigma_t * d_sigma_t
+
+        return -drift, diffusion
+
+    def compute_diffusion(self, x, t, form="constant", norm=1.0):
+        """Compute the diffusion term of the SDE
+        Args:
+          x: [batch_dim, ...], data point
+          t: [batch_dim,], time vector
+          form: str, form of the diffusion term
+          norm: float, norm of the diffusion term
+        """
+        t = expand_t_like_x(t, x)
+        choices = {
+            "constant": norm,
+            "SBDM": norm * self.compute_drift(x, t)[1],
+            "sigma": norm * self.compute_sigma_t(t)[0],
+            "linear": norm * (1 - t),
+            "decreasing": 0.25 * (norm * th.cos(np.pi * t) + 1) ** 2,
+            "inccreasing-decreasing": norm * th.sin(np.pi * t) ** 2,
+        }
+
+        try:
+            diffusion = choices[form]
+        except KeyError:
+            raise NotImplementedError(f"Diffusion form {form} not implemented")
+
+        return diffusion
+
+    def get_score_from_velocity(self, velocity, x, t):
+        """Wrapper function: transfrom velocity prediction model to score
+        Args:
+            velocity: [batch_dim, ...] shaped tensor; velocity model output
+            x: [batch_dim, ...] shaped tensor; x_t data point
+            t: [batch_dim,] time tensor
+        """
+        t = expand_t_like_x(t, x)
+        alpha_t, d_alpha_t = self.compute_alpha_t(t)
+        sigma_t, d_sigma_t = self.compute_sigma_t(t)
+        mean = x
+        reverse_alpha_ratio = alpha_t / d_alpha_t
+        var = sigma_t**2 - reverse_alpha_ratio * d_sigma_t * sigma_t
+        score = (reverse_alpha_ratio * velocity - mean) / var
+        return score
+
+    def get_noise_from_velocity(self, velocity, x, t):
+        """Wrapper function: transfrom velocity prediction model to denoiser
+        Args:
+            velocity: [batch_dim, ...] shaped tensor; velocity model output
+            x: [batch_dim, ...] shaped tensor; x_t data point
+            t: [batch_dim,] time tensor
+        """
+        t = expand_t_like_x(t, x)
+        alpha_t, d_alpha_t = self.compute_alpha_t(t)
+        sigma_t, d_sigma_t = self.compute_sigma_t(t)
+        mean = x
+        reverse_alpha_ratio = alpha_t / d_alpha_t
+        var = reverse_alpha_ratio * d_sigma_t - sigma_t
+        noise = (reverse_alpha_ratio * velocity - mean) / var
+        return noise
+
+    def get_velocity_from_score(self, score, x, t):
+        """Wrapper function: transfrom score prediction model to velocity
+        Args:
+            score: [batch_dim, ...] shaped tensor; score model output
+            x: [batch_dim, ...] shaped tensor; x_t data point
+            t: [batch_dim,] time tensor
+        """
+        t = expand_t_like_x(t, x)
+        drift, var = self.compute_drift(x, t)
+        velocity = var * score - drift
+        return velocity
+
+    def compute_mu_t(self, t, x0, x1):
+        """Compute the mean of time-dependent density p_t"""
+        t = expand_t_like_x(t, x1)
+        alpha_t, _ = self.compute_alpha_t(t)
+        sigma_t, _ = self.compute_sigma_t(t)
+        if isinstance(x1, (list, tuple)):
+            return [alpha_t[i] * x1[i] + sigma_t[i] * x0[i] for i in range(len(x1))]
+        else:
+            return alpha_t * x1 + sigma_t * x0
+
+    def compute_xt(self, t, x0, x1):
+        """Sample xt from time-dependent density p_t; rng is required"""
+        xt = self.compute_mu_t(t, x0, x1)
+        return xt
+
+    def compute_ut(self, t, x0, x1, xt):
+        """Compute the vector field corresponding to p_t"""
+        t = expand_t_like_x(t, x1)
+        _, d_alpha_t = self.compute_alpha_t(t)
+        _, d_sigma_t = self.compute_sigma_t(t)
+        if isinstance(x1, (list, tuple)):
+            return [d_alpha_t * x1[i] + d_sigma_t * x0[i] for i in range(len(x1))]
+        else:
+            return d_alpha_t * x1 + d_sigma_t * x0
+
+    def plan(self, t, x0, x1):
+        xt = self.compute_xt(t, x0, x1)
+        ut = self.compute_ut(t, x0, x1, xt)
+        return t, xt, ut
+
+
+class VPCPlan(ICPlan):
+    """class for VP path flow matching"""
+
+    def __init__(self, sigma_min=0.1, sigma_max=20.0):
+        self.sigma_min = sigma_min
+        self.sigma_max = sigma_max
+        self.log_mean_coeff = (
+            lambda t: -0.25 * ((1 - t) ** 2) * (self.sigma_max - self.sigma_min)
+            - 0.5 * (1 - t) * self.sigma_min
+        )
+        self.d_log_mean_coeff = (
+            lambda t: 0.5 * (1 - t) * (self.sigma_max - self.sigma_min)
+            + 0.5 * self.sigma_min
+        )
+
+    def compute_alpha_t(self, t):
+        """Compute coefficient of x1"""
+        alpha_t = self.log_mean_coeff(t)
+        alpha_t = th.exp(alpha_t)
+        d_alpha_t = alpha_t * self.d_log_mean_coeff(t)
+        return alpha_t, d_alpha_t
+
+    def compute_sigma_t(self, t):
+        """Compute coefficient of x0"""
+        p_sigma_t = 2 * self.log_mean_coeff(t)
+        sigma_t = th.sqrt(1 - th.exp(p_sigma_t))
+        d_sigma_t = th.exp(p_sigma_t) * (2 * self.d_log_mean_coeff(t)) / (-2 * sigma_t)
+        return sigma_t, d_sigma_t
+
+    def compute_d_alpha_alpha_ratio_t(self, t):
+        """Special purposed function for computing numerical stabled d_alpha_t / alpha_t"""
+        return self.d_log_mean_coeff(t)
+
+    def compute_drift(self, x, t):
+        """Compute the drift term of the SDE"""
+        t = expand_t_like_x(t, x)
+        beta_t = self.sigma_min + (1 - t) * (self.sigma_max - self.sigma_min)
+        return -0.5 * beta_t * x, beta_t / 2
+
+
+class GVPCPlan(ICPlan):
+    def __init__(self, sigma=0.0):
+        super().__init__(sigma)
+
+    def compute_alpha_t(self, t):
+        """Compute coefficient of x1"""
+        alpha_t = th.sin(t * np.pi / 2)
+        d_alpha_t = np.pi / 2 * th.cos(t * np.pi / 2)
+        return alpha_t, d_alpha_t
+
+    def compute_sigma_t(self, t):
+        """Compute coefficient of x0"""
+        sigma_t = th.cos(t * np.pi / 2)
+        d_sigma_t = -np.pi / 2 * th.sin(t * np.pi / 2)
+        return sigma_t, d_sigma_t
+
+    def compute_d_alpha_alpha_ratio_t(self, t):
+        """Special purposed function for computing numerical stabled d_alpha_t / alpha_t"""
+        return np.pi / (2 * th.tan(t * np.pi / 2))

transport/transport.py

@@ -0,0 +1,484 @@
+import torch as th
+import numpy as np
+import logging
+
+import enum
+
+from . import path
+from .utils import EasyDict, log_state, mean_flat
+from .integrators import ode, sde
+
+
+class ModelType(enum.Enum):
+    """
+    Which type of output the model predicts.
+    """
+
+    NOISE = enum.auto()  # the model predicts epsilon
+    SCORE = enum.auto()  # the model predicts \nabla \log p(x)
+    VELOCITY = enum.auto()  # the model predicts v(x)
+
+
+class PathType(enum.Enum):
+    """
+    Which type of path to use.
+    """
+
+    LINEAR = enum.auto()
+    GVP = enum.auto()
+    VP = enum.auto()
+
+
+class WeightType(enum.Enum):
+    """
+    Which type of weighting to use.
+    """
+
+    NONE = enum.auto()
+    VELOCITY = enum.auto()
+    LIKELIHOOD = enum.auto()
+
+
+class SNRType(enum.Enum):
+    UNIFORM = enum.auto()
+    LOGNORM = enum.auto()
+
+
+class Transport:
+
+    def __init__(
+        self, *, model_type, path_type, loss_type, train_eps, sample_eps, snr_type
+    ):
+        path_options = {
+            PathType.LINEAR: path.ICPlan,
+            PathType.GVP: path.GVPCPlan,
+            PathType.VP: path.VPCPlan,
+        }
+
+        self.loss_type = loss_type
+        self.model_type = model_type
+        self.path_sampler = path_options[path_type]()
+        self.train_eps = train_eps
+        self.sample_eps = sample_eps
+
+        self.snr_type = snr_type
+
+    def prior_logp(self, z):
+        """
+        Standard multivariate normal prior
+        Assume z is batched
+        """
+        shape = th.tensor(z.size())
+        N = th.prod(shape[1:])
+        _fn = lambda x: -N / 2.0 * np.log(2 * np.pi) - th.sum(x**2) / 2.0
+        return th.vmap(_fn)(z)
+
+    def check_interval(
+        self,
+        train_eps,
+        sample_eps,
+        *,
+        diffusion_form="SBDM",
+        sde=False,
+        reverse=False,
+        eval=False,
+        last_step_size=0.0,
+    ):
+        t0 = 0
+        t1 = 1
+        eps = train_eps if not eval else sample_eps
+        if type(self.path_sampler) in [path.VPCPlan]:
+
+            t1 = 1 - eps if (not sde or last_step_size == 0) else 1 - last_step_size
+
+        elif (type(self.path_sampler) in [path.ICPlan, path.GVPCPlan]) and (
+            self.model_type != ModelType.VELOCITY or sde
+        ):  # avoid numerical issue by taking a first semi-implicit step
+
+            t0 = (
+                eps
+                if (diffusion_form == "SBDM" and sde)
+                or self.model_type != ModelType.VELOCITY
+                else 0
+            )
+            t1 = 1 - eps if (not sde or last_step_size == 0) else 1 - last_step_size
+
+        if reverse:
+            t0, t1 = 1 - t0, 1 - t1
+
+        return t0, t1
+
+    def sample(self, x1):
+        """Sampling x0 & t based on shape of x1 (if needed)
+        Args:
+          x1 - data point; [batch, *dim]
+        """
+        if isinstance(x1, (list, tuple)):
+            x0 = [th.randn_like(img_start) for img_start in x1]
+        else:
+            x0 = th.randn_like(x1)
+        t0, t1 = self.check_interval(self.train_eps, self.sample_eps)
+
+        if self.snr_type == SNRType.UNIFORM:
+            t = th.rand((len(x1),)) * (t1 - t0) + t0
+        elif self.snr_type == SNRType.LOGNORM:
+            u = th.normal(mean=0.0, std=1.0, size=(len(x1),))
+            t = 1 / (1 + th.exp(-u)) * (t1 - t0) + t0
+        else:
+            raise ValueError(f"Unknown snr type: {self.snr_type}")
+        t = t.to(x1[0])
+        return t, x0, x1
+
+    def training_losses(self, model, x1, model_kwargs=None):
+        """Loss for training the score model
+        Args:
+        - model: backbone model; could be score, noise, or velocity
+        - x1: datapoint
+        - model_kwargs: additional arguments for the model
+        """
+        if model_kwargs == None:
+            model_kwargs = {}
+        t, x0, x1 = self.sample(x1)
+        t, xt, ut = self.path_sampler.plan(t, x0, x1)
+        model_output = model(xt, t, **model_kwargs)
+        B = len(x0)
+
+        terms = {}
+        # terms['pred'] = model_output
+        if self.model_type == ModelType.VELOCITY:
+            if isinstance(x1, (list, tuple)):
+                assert len(model_output) == len(ut) == len(x1)
+                for i in range(B):
+                    assert (
+                        model_output[i].shape == ut[i].shape == x1[i].shape
+                    ), f"{model_output[i].shape} {ut[i].shape} {x1[i].shape}"
+                terms["task_loss"] = th.stack(
+                    [((ut[i] - model_output[i]) ** 2).mean() for i in range(B)],
+                    dim=0,
+                )
+            else:
+                terms["task_loss"] = mean_flat(((model_output - ut) ** 2))
+        else:
+            raise NotImplementedError
+            # _, drift_var = self.path_sampler.compute_drift(xt, t)
+            # sigma_t, _ = self.path_sampler.compute_sigma_t(path.expand_t_like_x(t, xt))
+            # if self.loss_type in [WeightType.VELOCITY]:
+            #     weight = (drift_var / sigma_t) ** 2
+            # elif self.loss_type in [WeightType.LIKELIHOOD]:
+            #     weight = drift_var / (sigma_t ** 2)
+            # elif self.loss_type in [WeightType.NONE]:
+            #     weight = 1
+            # else:
+            #     raise NotImplementedError()
+            #
+            # if self.model_type == ModelType.NOISE:
+            #     terms['task_loss'] = mean_flat(weight * ((model_output - x0) ** 2))
+            # else:
+            #     terms['task_loss'] = mean_flat(weight * ((model_output * sigma_t + x0) ** 2))
+
+        terms["loss"] = terms["task_loss"]
+        terms["task_loss"] = terms["task_loss"].clone().detach()
+        return terms
+
+    def get_drift(self):
+        """member function for obtaining the drift of the probability flow ODE"""
+
+        def score_ode(x, t, model, **model_kwargs):
+            drift_mean, drift_var = self.path_sampler.compute_drift(x, t)
+            model_output = model(x, t, **model_kwargs)
+            return -drift_mean + drift_var * model_output  # by change of variable
+
+        def noise_ode(x, t, model, **model_kwargs):
+            drift_mean, drift_var = self.path_sampler.compute_drift(x, t)
+            sigma_t, _ = self.path_sampler.compute_sigma_t(path.expand_t_like_x(t, x))
+            model_output = model(x, t, **model_kwargs)
+            score = model_output / -sigma_t
+            return -drift_mean + drift_var * score
+
+        def velocity_ode(x, t, model, **model_kwargs):
+            model_output = model(x, t, **model_kwargs)
+            return model_output
+
+        if self.model_type == ModelType.NOISE:
+            drift_fn = noise_ode
+        elif self.model_type == ModelType.SCORE:
+            drift_fn = score_ode
+        else:
+            drift_fn = velocity_ode
+
+        def body_fn(x, t, model, **model_kwargs):
+            model_output = drift_fn(x, t, model, **model_kwargs)
+            assert (
+                model_output.shape == x.shape
+            ), "Output shape from ODE solver must match input shape"
+            return model_output
+
+        return body_fn
+
+    def get_score(
+        self,
+    ):
+        """member function for obtaining score of
+        x_t = alpha_t * x + sigma_t * eps"""
+        if self.model_type == ModelType.NOISE:
+            score_fn = (
+                lambda x, t, model, **kwargs: model(x, t, **kwargs)
+                / -self.path_sampler.compute_sigma_t(path.expand_t_like_x(t, x))[0]
+            )
+        elif self.model_type == ModelType.SCORE:
+            score_fn = lambda x, t, model, **kwagrs: model(x, t, **kwagrs)
+        elif self.model_type == ModelType.VELOCITY:
+            score_fn = (
+                lambda x, t, model, **kwargs: self.path_sampler.get_score_from_velocity(
+                    model(x, t, **kwargs), x, t
+                )
+            )
+        else:
+            raise NotImplementedError()
+
+        return score_fn
+
+
+class Sampler:
+    """Sampler class for the transport model"""
+
+    def __init__(
+        self,
+        transport,
+    ):
+        """Constructor for a general sampler; supporting different sampling methods
+        Args:
+        - transport: an tranport object specify model prediction & interpolant type
+        """
+
+        self.transport = transport
+        self.drift = self.transport.get_drift()
+        self.score = self.transport.get_score()
+
+    def __get_sde_diffusion_and_drift(
+        self,
+        *,
+        diffusion_form="SBDM",
+        diffusion_norm=1.0,
+    ):
+
+        def diffusion_fn(x, t):
+            diffusion = self.transport.path_sampler.compute_diffusion(
+                x, t, form=diffusion_form, norm=diffusion_norm
+            )
+            return diffusion
+
+        sde_drift = lambda x, t, model, **kwargs: self.drift(
+            x, t, model, **kwargs
+        ) + diffusion_fn(x, t) * self.score(x, t, model, **kwargs)
+
+        sde_diffusion = diffusion_fn
+
+        return sde_drift, sde_diffusion
+
+    def __get_last_step(
+        self,
+        sde_drift,
+        *,
+        last_step,
+        last_step_size,
+    ):
+        """Get the last step function of the SDE solver"""
+
+        if last_step is None:
+            last_step_fn = lambda x, t, model, **model_kwargs: x
+        elif last_step == "Mean":
+            last_step_fn = (
+                lambda x, t, model, **model_kwargs: x
+                + sde_drift(x, t, model, **model_kwargs) * last_step_size
+            )
+        elif last_step == "Tweedie":
+            alpha = (
+                self.transport.path_sampler.compute_alpha_t
+            )  # simple aliasing; the original name was too long
+            sigma = self.transport.path_sampler.compute_sigma_t
+            last_step_fn = lambda x, t, model, **model_kwargs: x / alpha(t)[0][0] + (
+                sigma(t)[0][0] ** 2
+            ) / alpha(t)[0][0] * self.score(x, t, model, **model_kwargs)
+        elif last_step == "Euler":
+            last_step_fn = (
+                lambda x, t, model, **model_kwargs: x
+                + self.drift(x, t, model, **model_kwargs) * last_step_size
+            )
+        else:
+            raise NotImplementedError()
+
+        return last_step_fn
+
+    def sample_sde(
+        self,
+        *,
+        sampling_method="Euler",
+        diffusion_form="SBDM",
+        diffusion_norm=1.0,
+        last_step="Mean",
+        last_step_size=0.04,
+        num_steps=250,
+    ):
+        """returns a sampling function with given SDE settings
+        Args:
+        - sampling_method: type of sampler used in solving the SDE; default to be Euler-Maruyama
+        - diffusion_form: function form of diffusion coefficient; default to be matching SBDM
+        - diffusion_norm: function magnitude of diffusion coefficient; default to 1
+        - last_step: type of the last step; default to identity
+        - last_step_size: size of the last step; default to match the stride of 250 steps over [0,1]
+        - num_steps: total integration step of SDE
+        """
+
+        if last_step is None:
+            last_step_size = 0.0
+
+        sde_drift, sde_diffusion = self.__get_sde_diffusion_and_drift(
+            diffusion_form=diffusion_form,
+            diffusion_norm=diffusion_norm,
+        )
+
+        t0, t1 = self.transport.check_interval(
+            self.transport.train_eps,
+            self.transport.sample_eps,
+            diffusion_form=diffusion_form,
+            sde=True,
+            eval=True,
+            reverse=False,
+            last_step_size=last_step_size,
+        )
+
+        _sde = sde(
+            sde_drift,
+            sde_diffusion,
+            t0=t0,
+            t1=t1,
+            num_steps=num_steps,
+            sampler_type=sampling_method,
+        )
+
+        last_step_fn = self.__get_last_step(
+            sde_drift, last_step=last_step, last_step_size=last_step_size
+        )
+
+        def _sample(init, model, **model_kwargs):
+            xs = _sde.sample(init, model, **model_kwargs)
+            ts = th.ones(init.size(0), device=init.device) * t1
+            x = last_step_fn(xs[-1], ts, model, **model_kwargs)
+            xs.append(x)
+
+            assert len(xs) == num_steps, "Samples does not match the number of steps"
+
+            return xs
+
+        return _sample
+
+    def sample_ode(
+        self,
+        *,
+        sampling_method="dopri5",
+        num_steps=50,
+        atol=1e-6,
+        rtol=1e-3,
+        reverse=False,
+        time_shifting_factor=None,
+    ):
+        """returns a sampling function with given ODE settings
+        Args:
+        - sampling_method: type of sampler used in solving the ODE; default to be Dopri5
+        - num_steps:
+            - fixed solver (Euler, Heun): the actual number of integration steps performed
+            - adaptive solver (Dopri5): the number of datapoints saved during integration; produced by interpolation
+        - atol: absolute error tolerance for the solver
+        - rtol: relative error tolerance for the solver
+        - reverse: whether solving the ODE in reverse (data to noise); default to False
+        """
+        if reverse:
+            drift = lambda x, t, model, **kwargs: self.drift(
+                x, th.ones_like(t) * (1 - t), model, **kwargs
+            )
+        else:
+            drift = self.drift
+
+        t0, t1 = self.transport.check_interval(
+            self.transport.train_eps,
+            self.transport.sample_eps,
+            sde=False,
+            eval=True,
+            reverse=reverse,
+            last_step_size=0.0,
+        )
+
+        _ode = ode(
+            drift=drift,
+            t0=t0,
+            t1=t1,
+            sampler_type=sampling_method,
+            num_steps=num_steps,
+            atol=atol,
+            rtol=rtol,
+            time_shifting_factor=time_shifting_factor,
+        )
+
+        return _ode.sample
+
+    def sample_ode_likelihood(
+        self,
+        *,
+        sampling_method="dopri5",
+        num_steps=50,
+        atol=1e-6,
+        rtol=1e-3,
+    ):
+        """returns a sampling function for calculating likelihood with given ODE settings
+        Args:
+        - sampling_method: type of sampler used in solving the ODE; default to be Dopri5
+        - num_steps:
+            - fixed solver (Euler, Heun): the actual number of integration steps performed
+            - adaptive solver (Dopri5): the number of datapoints saved during integration; produced by interpolation
+        - atol: absolute error tolerance for the solver
+        - rtol: relative error tolerance for the solver
+        """
+
+        def _likelihood_drift(x, t, model, **model_kwargs):
+            x, _ = x
+            eps = th.randint(2, x.size(), dtype=th.float, device=x.device) * 2 - 1
+            t = th.ones_like(t) * (1 - t)
+            with th.enable_grad():
+                x.requires_grad = True
+                grad = th.autograd.grad(
+                    th.sum(self.drift(x, t, model, **model_kwargs) * eps), x
+                )[0]
+                logp_grad = th.sum(grad * eps, dim=tuple(range(1, len(x.size()))))
+                drift = self.drift(x, t, model, **model_kwargs)
+            return (-drift, logp_grad)
+
+        t0, t1 = self.transport.check_interval(
+            self.transport.train_eps,
+            self.transport.sample_eps,
+            sde=False,
+            eval=True,
+            reverse=False,
+            last_step_size=0.0,
+        )
+
+        _ode = ode(
+            drift=_likelihood_drift,
+            t0=t0,
+            t1=t1,
+            sampler_type=sampling_method,
+            num_steps=num_steps,
+            atol=atol,
+            rtol=rtol,
+        )
+
+        def _sample_fn(x, model, **model_kwargs):
+            init_logp = th.zeros(x.size(0)).to(x)
+            input = (x, init_logp)
+            drift, delta_logp = _ode.sample(input, model, **model_kwargs)
+            drift, delta_logp = drift[-1], delta_logp[-1]
+            prior_logp = self.transport.prior_logp(drift)
+            logp = prior_logp - delta_logp
+            return logp, drift
+
+        return _sample_fn

transport/utils.py

@@ -0,0 +1,32 @@
+import torch as th
+
+
+class EasyDict:
+
+    def __init__(self, sub_dict):
+        for k, v in sub_dict.items():
+            setattr(self, k, v)
+
+    def __getitem__(self, key):
+        return getattr(self, key)
+
+
+def mean_flat(x):
+    """
+    Take the mean over all non-batch dimensions.
+    """
+    return th.mean(x, dim=list(range(1, len(x.size()))))
+
+
+def log_state(state):
+    result = []
+
+    sorted_state = dict(sorted(state.items()))
+    for key, value in sorted_state.items():
+        # Check if the value is an instance of a class
+        if "<object" in str(value) or "object at" in str(value):
+            result.append(f"{key}: [{value.__class__.__name__}]")
+        else:
+            result.append(f"{key}: {value}")
+
+    return "\n".join(result)