Project: 018_Learning_to_Discretize_Denoising_Diffusion_ODEs | Function: _train_to_match_prior (iclr)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** LD3 soft teacher forcing training implementation with LPIPS loss for learning optimal discretization by matching teacher solver outputs while allowing input perturbations

**KEY TERMS:** {
  "prior_timesteps": "Ψ*(xT) teacher solver reference outputs",
  "dis_model": "Ψξ student discretization model",
  "loss_time": "d(Ψξ(x'T), Ψ*(xT)) distance loss function",
  "times1": "τξ(i) learned time steps from student",
  "optimizer_lamb1": "gradient optimizer for ξ parameters"
}

**CONTEXT CODE:**         self._create_train_loader()

        # Training state
        self.cur_iter = 0
        self.cur_round = 0
        self.count_worse = 0
        self.count_min_lr1_hit = 0
        self.count_min_lr2_hit = 0
        self.best_loss = float("inf")

        # Other parameters
        self.patient = training_config.patient
        self.lr2_patient = training_config.lr2_patient
        self.no_v1 = training_config.no_v1
        self.win_rate = training_config.win_rate
        self.snapshot_path = model_config.snapshot_path
        os.makedirs(self.snapshot_path, exist_ok=True)
        self.visualize = training_config.visualize

        # Device and optimizer setup
        self._set_device(model_config.device)
        self.params1, self.params2 = self._initialize_params()
        self.optimizer_lamb1 = torch.optim.RMSprop(
            [self.params1],
            lr=training_config.lr_time_1,
            momentum=training_config.momentum_time_1,
            weight_decay=training_config.weight_decay_time_1,
        )
        self.optimizer_lamb2 = torch.optim.SGD(
            [self.params2], lr=training_config.lr_time_2
        )
        self.prior_timesteps = training_config.prior_timesteps
        self.match_prior = training_config.match_prior

        # Additional attributes
        self.solver_extra_params = model_config.solver_extra_params or {}
        self.lambda_min = self.noise_schedule.lambda_min
        self.lambda_max = self.noise_schedule.lambda_max
        self.time_max = self.noise_schedule.inverse_lambda(self.lambda_min)
        self.time_min = self.noise_schedule.inverse_lambda(self.lambda_max)

        # Initialize baseline
        self._compute_baseline()

        # Initialize loss function
        self.loss_type = training_config.loss_type
        self.loss_fn = self._initialize_loss_fn()
        self.loss_vector = None


    def _train_to_match_prior(self, prior_timesteps=None):
        raise NotImplementedError("Function implementation has been masked for testing")
    
    def _initialize_loss_fn(self):
        if self.loss_type == 'LPIPS':
            return lpips.LPIPS(net='vgg').to(self.device)
        elif self.loss_type == 'L2':
            return lambda x, y : compute_distance_between_two(x, y, self.channels, self.resolution)
        elif self.loss_type == 'L1':
            return lambda x, y: compute_distance_between_two_L1(x, y, self.channels, self.resolution)
        else:
            raise NotImplementedError
    
    def _initialize_params(self):
        params1 = torch.nn.Parameter(torch.ones(self.steps + 1, dtype=torch.float32).cuda(), requires_grad=True)
        params2 = torch.nn.Parameter(torch.zeros(self.steps + 1, dtype=torch.float32).cuda(), requires_grad=True)
        return params1, params2

    def _set_device(self, device):
        self.device = device or torch.device("cuda" if torch.cuda.is_available() else "cpu")

    def _create_valid_loaders(self):
        self.valid_loader = DataLoader(self.valid_data, batch_size=self.train_batch_size, shuffle=False, collate_fn=custom_collate_fn)
        self.valid_only_loader = DataLoader(self.valid_data, batch_size=self.valid_batch_size, shuffle=False, collate_fn=custom_collate_fn)

    def _create_train_loader(self):
        self.train_loader = DataLoader(self.train_data, batch_size=self.train_batch_size, shuffle=True, collate_fn=custom_collate_fn)
    
    def _solve_ode(self, timesteps=None, img=None, latent=None, condition=None, uncondition=None, valid=False):
        batch_size = latent.shape[0]
        latent = latent.reshape(batch_size, self.channels, self.resolution, self.resolution)
        dis_model = discretize_model_wrapper(
            self.params1,
            self.params2,
            self.lambda_max,
            self.lambda_min,
            self.noise_schedule,
            self.time_mode,
            self.win_rate,
        )

        if timesteps is None:
            timesteps1, timesteps2 = dis_model()
        else:
            timesteps1 = timesteps
            timesteps2 = timesteps

        if not valid and timesteps is None:
            tst = torch.cat([timesteps1, timesteps2], dim=0).detach().cpu()
            torch.save(tst, os.path.join(self.snapshot_path, f"t_steps.pt"))

        self.t_steps1 = timesteps1.detach()
        self.t_steps2 = timesteps2.detach()
        lamb1 = self.noise_schedule.marginal_lambda(timesteps1)
        lamb2 = self.noise_schedule.marginal_lambda(timesteps2)
        self.logSNR1 = lamb1.detach().cpu()
        self.logSNR2 = lamb2.detach().cpu()

        x_next_ = self.noise_schedule.prior_transformation(latent)  # bs x 3 x 32 x 32
        x_next_ = self.solver.sample_simple(
            model_fn=self.net,
            x=x_next_,
            timesteps=timesteps1,
            timesteps2=timesteps2,
            order=self.order,
            NFEs=self.steps,
            condition=condition,
            unconditional_condition=uncondition,
            **self.solver_extra_params,
        )
        x_next_ = self.decoding_fn(x_next_)
        self.loss_vector = self.loss_fn(img.float(), x_next_.float()).squeeze()
        loss = self.loss_vector.mean()
        logging.info(f"{self._current_version} Loss: {loss.item()}")

        return loss, x_next_.float(), img.float()


    @property
    def _current_version(self):
        return 'Ver1' if self._is_in_version_1() else 'Ver2'

    def _is_in_version_1(self):
        return self.cur_round < self.training_rounds_v1

    def _compute_baseline(self):
        self.straight_line = torch.linspace(self.lambda_min, self.lambda_max, self.steps + 1)
        self.time_logSNR = self.noise_schedule.inverse_lambda(self.straight_line).to(self.device)        
        time_max = self.noise_schedule.inverse_lambda(self.lambda_min)
        time_min = self.noise_schedule.inverse_lambda(self.lambda_max)
        self.time_s = torch.linspace(time_max.item(), time_min.item(), 1000)
        self.time_straight = torch.linspace(time_max.item(), time_min.item(), self.steps + 1)
        self.time_straight = self.time_straight.to(self.device)
        self.straight_time = self.noise_schedule.marginal_lambda(self.time_s)
        t_order = 2
        self.time_q = torch.linspace((time_max**(1/t_order)).item(), (time_min**(1/t_order)).item(), 1000)**t_order
        self.quadratic_time = torch.linspace((time_max**(1/t_order)).item(), (time_min**(1/t_order)).item(), self.steps + 1)**t_order

        self.quadratic_time = self.quadratic_time.to(self.device)
        self.time_quadratic = self.noise_schedule.marginal_lambda(self.time_q)


Complete the function implementation replacing "raise NotImplementedError".