def _vb_terms_bpd(self, model, x_start, x_t, t, clip_denoised=False, model_kwargs=None):
        """
        Get a term for the variational lower-bound.

        The resulting units are bits (rather than nats, as one might expect).
        This allows for comparison to other papers.

        :return: a dict with the following keys:
                 - 'output': a shape [N] tensor of NLLs or KLs.
                 - 'pred_xstart': the x_0 predictions.
        """
        true_mean, _, true_log_variance_clipped = self.q_posterior_mean_variance(
            x_start=x_start, x_t=x_t, t=t
        )
        out = self.p_mean_variance(
            model, x_t, t, clip_denoised=clip_denoised, model_kwargs=model_kwargs
        )
        kl = normal_kl(true_mean, true_log_variance_clipped, out["mean"], out["log_variance"])
        kl = mean_flat(kl) / np.log(2.0)

        decoder_nll = -discretized_gaussian_log_likelihood(
            x_start, means=out["mean"], log_scales=0.5 * out["log_variance"]
        )
        if not self.discretized_t0:
            decoder_nll = th.zeros_like(decoder_nll)
        assert decoder_nll.shape == x_start.shape
        decoder_nll = mean_flat(decoder_nll) / np.log(2.0)

        # At the first timestep return the decoder NLL,
        # otherwise return KL(q(x_{t-1}|x_t,x_0) || p(x_{t-1}|x_t))
        output = th.where((t == 0), decoder_nll, kl)
        return {
            "output": output,
            "pred_xstart": out["pred_xstart"],
            "extra": out["extra"],
        }

        Get a term for the variational lower-bound.

        The resulting units are bits (rather than nats, as one might expect).
        This allows for comparison to other papers.

        :return: a dict with the following keys:
                 - 'output': a shape [N] tensor of NLLs or KLs.
                 - 'pred_xstart': the x_0 predictions.
        
shap_e/diffusion/gaussian_diffusion.py