add second_order to samplers that mistakenly didn't have it

    ('Euler', 'sample_euler', ['k_euler'], {}),

    ('LMS', 'sample_lms', ['k_lms'], {}),

    ('Heun', 'sample_heun', ['k_heun'], {"second_order": True}),

    ('DPM2', 'sample_dpm_2', ['k_dpm_2'], {'discard_next_to_last_sigma': True}),

    ('DPM2 a', 'sample_dpm_2_ancestral', ['k_dpm_2_a'], {'discard_next_to_last_sigma': True, "uses_ensd": True}),

    ('DPM2', 'sample_dpm_2', ['k_dpm_2'], {'discard_next_to_last_sigma': True, "second_order": True}),

    ('DPM2 a', 'sample_dpm_2_ancestral', ['k_dpm_2_a'], {'discard_next_to_last_sigma': True, "uses_ensd": True, "second_order": True}),

    ('DPM++ 2S a', 'sample_dpmpp_2s_ancestral', ['k_dpmpp_2s_a'], {"uses_ensd": True, "second_order": True}),

    ('DPM++ 2M', 'sample_dpmpp_2m', ['k_dpmpp_2m'], {}),

    ('DPM++ SDE', 'sample_dpmpp_sde', ['k_dpmpp_sde'], {"second_order": True, "brownian_noise": True}),

    ('DPM2 Karras', 'sample_dpm_2', ['k_dpm_2_ka'], {'scheduler': 'karras', 'discard_next_to_last_sigma': True, "uses_ensd": True, "second_order": True}),

    ('DPM2 a Karras', 'sample_dpm_2_ancestral', ['k_dpm_2_a_ka'], {'scheduler': 'karras', 'discard_next_to_last_sigma': True, "uses_ensd": True, "second_order": True}),

    ('DPM++ 2S a Karras', 'sample_dpmpp_2s_ancestral', ['k_dpmpp_2s_a_ka'], {'scheduler': 'karras', "uses_ensd": True, "second_order": True}),

    ('Restart', sd_samplers_extra.restart_sampler, ['restart'], {'scheduler': 'karras'}),

    ('Restart', sd_samplers_extra.restart_sampler, ['restart'], {'scheduler': 'karras', "second_order": True}),

]